The 45-year-old Uruguayan has signed a two-year deal and will take charge with immediate effect, the club has confirmed.
The former Brighton manager's initial challenge will be to secure a first Premier League win of the season with the Black Cats currently lying at the foot of the table with just one point from their first seven games, a return which leaves them six adrift of safety.
Poyet's arrival at the Stadium of Light, where he becomes the sixth permanent manager in less than five years - his official title, like that of predecessor Di Canio, will be head coach - was confirmed on Tuesday morning.
Owner Ellis Short, who took more than a fortnight to find the right man, said: "We analysed a wide range of candidates and believe that Gus' track record, experience, commitment and passion make him the right man to take us forward."
"We welcome him to Sunderland."
The former Chelsea and Tottenham midfielder, who will be joined by staff Mauricio Taricco and Charlie Oatway, has been out of the game since parting company with the Seagulls during the summer on less that friendly terms.
His track record as a manager is limited to his experience with the South Coast club and Sunderland have given him his first chance to work in the English top flight, although he had earlier been part of coaching set-ups at Swindon, Leeds and Tottenham.
However, his record at Brighton was impressive, having guided them to the League One title at the end of the 2010-11 season and into the Championship play-offs at the end of the last campaign before his untimely departure.
Poyet will be required to work within the system installed by Short after Di Canio's arrival with the Texan businessman determined to continue despite the failings of the Italian's brief and often chaotic reign.
That will mean working under director of football Roberto De Fanti in an attempt to provide the club with long-term future success.
De Fanti and chief scout Valentino Angeloni recruited no fewer than 14 signings during the summer transfer window, several of them ostensibly for the development squad.
However, Di Canio, who was at the helm for only 13 games and 175 days, was still in the process of moulding his new-look squad into a unit when he was relieved of his duties after his relationship with some of his players hit rock-bottom.
Poyet will now take up the baton with the Black Cats at least having shown promising signs of gelling under interim head coach Kevin Ball in recent weeks.
A 2-0 Capital One Cup victory over League One Peterborough got the 48-year's temporary spell in charge off to a positive start, and their performances in defeat by Liverpool and particularly Manchester United since have suggested a corner is close to being turned.
Poyet will have the international break during which to work with those players not representing their countries before sending a team out for the first time at Swansea a week on Saturday.
Intriguingly, his second game, as was Di Canio's, will be a derby clash with Newcastle, and a repeat on Wearside of the 3-0 win the Black Cats secured at St James' Park in April would provide the perfect launch-pad for his tenure.