The Uruguayan joins the Black Cats on a two-year deal as head coach, and will look to lift the club off the bottom of the Premier League after Paolo Di Canio's disastrous spell
The Uruguayan had been a long-term favourite 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 defeat to Liverpool and Manchester United.
Short said of the appointment: “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 added: “It's a huge challenge but one I am excited about and I am grateful for the opportunity to manage in the Barclays Premier League.
“I think the key behind my strong home record at Brighton was the connection with the fans - I can see that here also.
“I look forward to proving my ability to the fans - I want them to believe because we need to stick together.
"I hope at the end of the season we will be sitting here smiling. When you are at the bottom, everyone will say it will be very difficult. The idea here is to believe, to be convinced.
"From what I see, I do believe we can get safe. Now, I must convince the players.
"We must all understand that we really have to believe in this opportunity we start today. I will ask for help, as you can imagine, but it is my job to get everyone to commit."
Sunderland currently sit bottom of the Premier League having taken just one point from their first seven matches - they 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 after the international break, with a Tyne-Wear derby clash against Newcastle United just eight days later.