The Uruguayan will be tasked with turning things around for the Black Cats, who only have one point from their first seven Premier League games.
The former Brighton and Hove Albion boss had been a long-term favorite to succeed Paolo Di Canio, who was relieved of his duties last month.
Poyet held talks with Sunderland owner Ellis Short following Di Canio's dismissal and has now been chosen ahead of other candidates including caretaker boss Kevin Ball, who oversaw encouraging displays in defeats to Liverpool and Manchester United.
Short said of the appointment: “We analyzed a wide range of candidates and believe that Gus's track record, experience, commitment and passion make him the right man to take us forward."
“We welcome him to Sunderland.”
Sunderland currently sits bottom of the Premier League having taken just one point from its first seven matches. The Black Cats have not won a league game since a 1-0 triumph over Everton on April 20.
Poyet, who managed Brighton for three and a half years before being sacked in May, will become the first Uruguayan to manage in England's top-flight. The 45-year-old has previously served as first-team coach to Juande Ramos at Tottenham.
His first task will be to prepare his side to face Swansea City after the international break, with a Tyne-Wear derby clash against Newcastle United just eight days later.
U.S. international Jozy Altidore has gotten off to a slow goalscoring start with the Black Cats, with zero goals in six Premier League games and one goal in the Capital One Cup.