The Uruguayan was confirmed as the Black Cats' new manager this morning on a two-year deal, replacing Paolo Di Canio, who was sacked five games into the Premier League season.
The 45-year-old became an early frontrunner following the Italian's dismissal, but some fans have expressed their discontent at the former Brighton & Hove Albion manager's arrival.
"I look forward to proving my ability to the fans," Poyet told the club's official website. "I want them to believe because we need to stick together.
"I think the key behind my strong home record at Brighton was the connection with the fans, I can see that here also.
"It's a huge challenge but one I am excited about and I am grateful for the opportunity to manage in the Premier League."
The North-East outfit currently sit at the bottom of the league table, having taken just one point from seven games.