The former Blues midfielder was surprisingly sacked as Carlo Ancelotti's No 2 last month.
He has been negotiating a pay-off with the Barclays Premier League champions and has now come to a resolution.
All over: Ray Wilkins (right) was axed as Carlo Ancelotti's right-hand man
He said: 'It has obviously been a big wrench leaving such an illustrious club and one which has played such a huge role in my playing and coaching career.
'I have great affection for the club, the staff, the players and its supporters and wish them all the very best for the remainder of this season and the future.
'I would also like to thank the club and the League Managers Association for ensuring that matters have been brought to a swift and harmonious conclusion.'
LMA chief executive Richard Bevan said: 'All parties are delighted that an agreement has been reached in a cordial and professional manner. I am sure that a manager of Ray's experience will be back involved in a managerial or coaching capacity soon.'
Wilkins abruptly left Stamford Bridge on November 11 after being told his contract, which was due to expire at the end of the season, would not be renewed.
He was replaced a week later by Michael Emenalo, Chelsea's former opposition scout.
New man: Michael Emenalo has been installed as Ancelotti's assistant
Ancelotti raised doubts about the Nigerian's role when he said Emenalo would not actually be involved in coaching the first team, although he has sat on the bench during matches.
Despite the resolution, there remain plenty of unanswered questions about Wilkins' exit. Ancelotti made it clear two weeks ago the decisions to remove the former England captain and install Emenalo were not his own and the Italian was forced to deny reports he was considering his own position.
Ancelotti will also lose sporting director Frank Arnesen at the end of the season, with the Dane having announced his resignation at the weekend.
Arnesen was keen to stress he had not been forced out of the club by billionaire owner Roman Abramovich, insisting moving on was entirely his own decision.
Ray Wilkins axed as Chelsea boss Carlo Ancelotti's right-hand man EXCLUSIVE: Arnesen out: More turmoil at Chelsea as Carlo aide calls time
Explore more:People: Carlo Ancelotti, Roman Abramovich, Frank Arnesen Places: United Kingdom