The Uruguayan, formerly in charge of Brighton & Hove Albion, succeeds Paolo Di Canio, who was fired on September 22 due to the club's poor performance.
Sunderland chairman Ellis Short said: "We analysed 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."
Poyet, 42, will be joined at the Stadium of Light by his backroom staff Mauricio Taricco and Charlie Oatway.
The Black Cats are propping up the Premier League standings with just one point from their first seven games.