The Sunderland manager was dismissed in June over an alleged incident of gross misconduct.
He appealed the decision to Brighton's board, but that was rejected, and he then took up the option to go down a legal route by taking the club to a tribunal.
But a statement made by a legal representative on behalf of Mr Poyet read: "In relation to Mr Gus Poyet's departure from Brighton Football Club, both Mr Gus Poyet and Brighton Football Club have now reached a settlement whereby Mr Gus Poyet has withdrawn his Employment Tribunal Claim.
"Mr Gus Poyet would like to take this opportunity to express his sincere thanks to Brighton Football Club and in particular the fans for the tremendous support received during his time as manager at Brighton Football Club.
"Mr Gus Poyet wishes both Brighton Football Club and the fans well for the future."
Capital One Cup drawFifth-round draw:
Leicester v Manchester CityStoke v Manchester UnitedSunderland v ChelseaTottenham v West Ham
Ties to be played week commencing December 16.It's usually at this stage the big clubs start taking the competition seriously, but there is no mistaking, the match with Chelsea certainly brightens up (what has been) a difficult season.
Sunderland Fixtures Sunday November 1014:05 Premier LeagueSunderland v Manchester City Saturday November 2315:00 Premier LeagueStoke City v Sunderland Saturday November 3015:00 Premier LeagueAston Villa v Sunderland 2012/13 SUNDERLAND 1 MAN CITY 0 2. Simon Mignolet 7. Sebastian Larsson 78' 24. Carlos Cuellar 12. Matthew Kilgallon 3. Danny Rose 88' 8. Craig Gardner 23. James McClean 14. Jack Colback 21. Adam Johnson 28. Stephane Sessegnon 26. Steven Fletcher Subs: 20. Keiren Westwood 2. Phil Bardsley 88' 9. Fraizer Campbell 78' 10. Connor Wickham 11. James McFadden 15. David Vaughan 19. Titus BrambleAdam Johnson came back to haunt Manchester City as the champions slipped to a third successive 1-0 Barclays Premier League defeat at Sunderland. The England winger, who was considered surplus to requirements at the Etihad Stadium during the summer and was allowed to join the Black Cats in a £10million move, embarrassed former team-mate Joe Hart with a dipping 53rd-minute strike which beat him at the near post and clinched three precious points for his new employers.
However, the winner was not without controversy with the visitors adamant they should have been awarded a free-kick for a foul on Pablo Zabaleta during the build-up.
Sunderland turned in one of their best displays of the season on a day when City played only fitfully, and Hart had to turn away Steven Fletcher's skidding effort and keep out Stephane Sessegnon 10 minutes from time.
However, if Johnson was the hero in front of a delighted Boxing Day crowd of 42,190, keeper Simon Mignolet deserved equal praise.
The Belgian denied Yaya Toure and David Silva before the break and Sergio Aguero after it to claim a precious clean sheet and make a huge contribution towards the win.
City arrived determined not to complete an unwanted hat-trick of 1-0 league defeats on Wearside and, after a lacklustre start, eased themselves into the game.
They might have been ahead with just eight minutes gone, but Vincent Kompany's header came back off the crossbar and Yaya Toure's goalbound follow-up was hacked away by Mignolet, who reacted instantly to deny the visitors an early lead.
Silva curled a 10th-minute free-kick wastefully over the bat and Toure saw a curling effort plucked from underneath the crossbar by Mignolet three minutes later.
City were pinning Sunderland deep inside their own half and it seemed only a matter of time before they made the pressure tell.
Mignolet had to be at his best once again with 24 minutes gone after Carlos Tevez and Aguero combined to put Silva in on goal, only for Mignolet to block his effort at close range.
But seconds later Hart had to dive to his right to turn away Fletcher's rasping left-foot drive and the Black Cats, buoyed after weathering the early storm, started to force their way into the game.
Johnson was enjoying the better of his individual battle with Zabaleta, who played much of the half with a heavily bandaged head after suffering a cut, and as James McClean took up the theme, Martin O'Neill's men upped their tempo.
Kompany and Matija Nastasic had to repel dangerous crosses from Sebastian Larsson and McClean respectively, and Sessegnon flashed a header well wide from Craig Gardner's driven 42nd-minute cross.
Larsson drilled a late free-kick straight into the defensive wall, but he and his team-mates left the pitch at the break with their clean sheet intact and everything still to play for.
Sunderland picked up where they had left off after the restart as McClean and Johnson, with the help of Sessegnon and Fletcher, stretched City uncomfortably at times. It was they who took the lead with eight minutes of the half played.
City boss Roberto Mancini and Zabaleta were left appealing in vain for a free-kick for Gardner's challenge on the full-back, but Johnson picked up possession and cut inside before blasting in a dipping shot which caught Hart flat-footed at his near post and squirmed into the bottom corner.
Sessegnon might have doubled his side's advantage within two minutes, but pulled his effort across the face of goal with City in disarray.
The visitors were almost breached once again on the hour when McClean picked out Sessegnon in front of goal, but the Benin international could not take the ball in his stride.
Kompany, who had already been booked, was fortunate to escape a second yellow card for a block on McClean as City struggled to contain a Black Cats side growing in confidence by the minute.
But the visitors gradually regained their composure and started to move the ball confidently once again and Mignolet had to claim a 68th-minute Zabaleta cross at his near post after being played in by James Milner.
The Belgium international excelled himself once again two minutes later to deny Aguero one on one, but it was Hart in the firing line with 10 minutes remaining when Sessegnon was played in by substitute Fraizer Campbell with the keeper coming out on top.
City battered away at their hosts as time ran down, but with Sunderland defending deep and with tenacity, they simply could not find a way through and McClean almost served up the perfect finish with an 88th-minute shot which flew just wide.
BLACK CATS v CITY 2012/2013 Wed 26 Dec Sunderland 1 - 0 Man. City Premier League Sat 06 Oct Man. City 3 - 0 Sunderland Premier League 2011/2012 Sat 31 Mar Man. City 3 - 3 Sunderland Premier League Sun 01 Jan Sunderland 1 - 0 Man. City Premier League 2010/2011 Sun 03 Apr Man. City 5 - 0 Sunderland Premier League Sun 29 Aug Sunderland 1 - 0 Man. City Premier League 2009/2010 Sun 14 Mar Sunderland 1 - 1 Man. City Premier League Sat 19 Dec Man. City 4 - 3 Sunderland Premier League 2008/2009 Sun 22 Mar Man. City 1 - 0 Sunderland Premier League Sun 31 Aug Sunderland 0 - 3 Man. City Premier League 2007/2008 Sat 12 Apr Sunderland 1 - 2 Man. City Premier League Mon 05 Nov Man. City 1 - 0 Sunderland Premier League 2005/2006 Sun 05 Mar Man. City 2 - 1 Sunderland Premiership Tue 23 Aug Sunderland 1 - 2 Man. City Premiership 2002/2003 Mon 21 Apr Man. City 3 - 0 Sunderland Premiership Mon 09 Dec Sunderland 0 - 3 Man. City Premiership 2000/2001 Sat 23 Dec Sunderland 1 - 0 Man. City Premiership Wed 23 Aug Man. City 4 - 2 Sunderland Premiership 1997/1998 Sat 17 Jan Man. City 0 - 1 Sunderland League Division One Fri 15 Aug Sunderland 3 - 1 Man. City League Division One 1990/1991 Sat 11 May Man. City 3 - 2 Sunderland First Division Sat 03 Nov Sunderland 1 - 1 Man. City First Division 1988/1989 Tue 14 Mar Sunderland 2 - 4 Man. City Second Division Sat 29 Oct Man. City 1 - 1 Sunderland Second Division 1982/1983 Sat 26 Feb Sunderland 3 - 2 Man. City First Division Sat 16 Oct Man. City 2 - 2 Sunderland First Division 1981/1982 Sat 15 May Sunderland 1 - 0 Man. City First Division Sat 19 Dec Man. City 2 - 3 Sunderland First Division 1980/1981 Wed 12 Nov Sunderland 2 - 0 Man. City First Division Wed 20 Aug Man. City 0 - 4 Sunderland First Division 1976/1977 Wed 09 Mar Man. City 1 - 0 Sunderland First Division Sat 18 Sep Sunderland 0 - 2 Man. City First Division 1969/1970 Sat 04 Apr Man. City 0 - 1 Sunderland First Division Wed 27 Aug Sunderland 0 - 4 Man. City First Division 1968/1969 Sat 12 Apr Man. City 1 - 0 Sunderland First Division Sat 21 Sep Sunderland 0 - 4 Man. City First Division 1967/1968 Sat 24 Feb Man. City 1 - 0 Sunderland First Division Sat 07 Oct Sunderland 1 - 0 Man. City First Division 1966/1967 Sat 31 Dec Sunderland 1 - 0 Man. City First Division Sat 27 Aug Man. City 1 - 0 Sunderland First Division 1963/1964 Sat 18 Jan Man. City 0 - 3 Sunderland Second Division Sat 14 Sep Sunderland 2 - 0 Man. City Second Division 1957/1958 Sat 12 Apr Man. City 3 - 1 Sunderland First Division Sat 30 Nov Sunderland 2 - 1 Man. City First Division 1956/1957 Sat 12 Jan Sunderland 1 - 1 Man. City First Division Sat 08 Sep Man. City 3 - 1 Sunderland First Division 1955/1956 Mon 02 Apr Man. City 4 - 2 Sunderland First Division Fri 30 Mar Sunderland 0 - 3 Man. City First Division 1954/1955 Sat 09 Apr Man. City 1 - 0 Sunderland First Division Sat 04 Dec Sunderland 3 - 2 Man. City First Division 1953/1954 Sat 02 Jan Man. City 2 - 1 Sunderland First Division Sat 29 Aug Sunderland 4 - 5 Man. City First Division 1952/1953 Sat 21 Mar Sunderland 3 - 3 Man. City First Division Sat 01 Nov Man. City 2 - 5 Sunderland First Division 1951/1952 Sat 22 Dec Man. City 3 - 1 Sunderland First Division Sat 25 Aug Sunderland 3 - 0 Man. City First Division 1949/1950 Sat 15 Apr Sunderland 1 - 2 Man. City First Division Sat 29 Oct Man. City 2 - 1 Sunderland First Division 1948/1949 Sat 16 Apr Man. City 1 - 1 Sunderland First Division Sat 23 Oct Sunderland 3 - 0 Man. City First Division 1947/1948 Sat 17 Jan Sunderland 0 - 1 Man. City First Division Sat 06 Sep Man. City 3 - 0 Sunderland First Division 1937/1938 Wed 02 Feb Man. City 0 - 0 Sunderland First Division Sat 11 Sep Sunderland 3 - 1 Man. City First Division 1936/1937 Wed 14 Apr Sunderland 1 - 3 Man. City First Division Sat 31 Oct Man. City 2 - 4 Sunderland First Division 1935/1936 Sat 04 Jan Man. City 0 - 1 Sunderland First Division Sat 07 Sep Sunderland 2 - 0 Man. City First Division 1934/1935 Wed 10 Apr Man. City 1 - 0 Sunderland First Division Sat 10 Nov Sunderland 3 - 2 Man. City First Division 1933/1934 Wed 11 Apr Sunderland 0 - 0 Man. City First Division Sat 04 Nov Man. City 4 - 1 Sunderland First Division 1932/1933 Sat 31 Dec Man. City 2 - 4 Sunderland First Division Sat 27 Aug Sunderland 3 - 2 Man. City First Division 1931/1932 Sat 02 Jan Sunderland 2 - 5 Man. City First Division Sat 29 Aug Man. City 1 - 1 Sunderland First Division 1930/1931 Sat 27 Dec Man. City 2 - 0 Sunderland First Division Sat 30 Aug Sunderland 3 - 3 Man. City First Division 1929/1930 Sat 04 Jan Man. City 2 - 2 Sunderland First Division Sat 07 Sep Sunderland 5 - 2 Man. City First Division 1928/1929 Sat 16 Feb Sunderland 3 - 1 Man. City First Division Sat 06 Oct Man. City 5 - 3 Sunderland First Division 1925/1926 Sat 13 Feb Sunderland 5 - 3 Man. City First Division Sat 03 Oct Man. City 4 - 1 Sunderland First Division 1924/1925 Sat 21 Mar Man. City 1 - 3 Sunderland First Division Sat 15 Nov Sunderland 3 - 2 Man. City First Division 1923/1924 Sat 29 Sep Sunderland 5 - 2 Man. City First Division Sat 22 Sep Man. City 4 - 1 Sunderland First Division 1922/1923 Mon 02 Apr Man. City 1 - 0 Sunderland First Division Fri 30 Mar Sunderland 2 - 0 Man. City First Division 1921/1922 Sat 14 Jan Sunderland 2 - 3 Man. City First Division Sat 31 Dec Man. City 3 - 0 Sunderland First Division 1920/1921 Sat 01 Jan Man. City 3 - 1 Sunderland First Division Sat 18 Dec Sunderland 1 - 0 Man. City First Division 1919/1920 Sat 27 Dec Man. City 1 - 0 Sunderland First Division Sat 20 Dec Sunderland 2 - 1 Man. City First Division 1914/1915 Sat 06 Mar Man. City 2 - 0 Sunderland First Division Sat 31 Oct Sunderland 0 - 2 Man. City First Division 1913/1914 Wed 18 Mar Man. City 3 - 1 Sunderland First Division Sat 18 Oct Sunderland 0 - 0 Man. City First Division 1912/1913 Sat 22 Mar Sunderland 1 - 0 Man. City First Division Sat 16 Nov Man. City 1 - 0 Sunderland First Division 1911/1912 Sat 30 Mar Man. City 2 - 0 Sunderland First Division Sat 25 Nov Sunderland 1 - 1 Man. City First Division 1910/1911 Sat 25 Feb Sunderland 4 - 0 Man. City First Division Sat 22 Oct Man. City 3 - 3 Sunderland First Division 1908/1909 Fri 09 Apr Sunderland 2 - 0 Man. City First Division Tue 01 Sep Man. City 1 - 0 Sunderland First Division 1907/1908 Sat 14 Sep Man. City 0 - 0 Sunderland First Division Mon 02 Sep Sunderland 2 - 5 Man. City First Division 1906/1907 Sat 27 Apr Man. City 2 - 3 Sunderland First Division Sat 22 Dec Sunderland 1 - 1 Man. City First Division 1905/1906 Sat 21 Apr Man. City 5 - 1 Sunderland First Division Sat 16 Dec Sunderland 2 - 0 Man. City First Division 1904/1905 Sat 01 Apr Sunderland 0 - 0 Man. City First Division Sat 03 Dec Man. City 5 - 2 Sunderland First Division 1903/1904 Sat 02 Apr Man. City 2 - 1 Sunderland First Division Sat 05 Dec Sunderland 1 - 1 Man. City First Division 1901/1902 Sat 04 Jan Man. City 0 - 3 Sunderland First Division Sat 07 Sep Sunderland 1 - 0 Man. City First Division 1900/1901 Tue 25 Dec Man. City 1 - 1 Sunderland First Division Sat 20 Oct Sunderland 3 - 0 Man. City First Division 1899/1900 Sat 14 Apr Sunderland 3 - 1 Man. City First Division Sat 09 Dec Man. City 2 - 1 Sunderland First Division
Source: Sunderland-Mad
Source: FOOTYMAD
