Poyet has been the favorite for the post since Roberto Di Matteo told Sunderland that he was not interested in taking the job, which the former Chelsea manager regards as a step down from the type of job he wants.
Sunderland chairman Ellis Short has been keen to lead a thorough process to find the new boss and it seems that the job has now been offered to Poyet, who has been out of football management since he was sacked by Brighton & Hove Albion at the end of last season.
Short and the Sunderland board had put the club's Under-21s manager, Kevin Ball, in caretaker charge for three games against Peterborough United, Liverpool and Manchester United.
Ball has helped to stabilize the squad and Poyet will now be charged with maintaining the Black Cats' Premier League status. Sunderland is rooted to the bottom of the table after collecting just a single point from its opening seven league fixtures of the season.
Writing in the matchday program ahead of Saturday's defeat to United, Short said: "Here at the club, like every supporter, we would like to see long-term success on the pitch and stability at the club. Unfortunately sometimes the quest for stability can be interrupted by the absolute necessity of staying in the league. This is because the long-term aim becomes irrelevant if we aren't at the top level.
"We now have a very important decision to make. Our only consideration in making that decision is what is best for the club. In doing so, we feel the weight of the entire city and beyond, along with the history of this massive football club."
Italian director of football Roberto De Fanti had targeted Di Matteo as his top choice but subsequently gave his backing to Poyet, who is regarded by Sunderland as a steady pair of hands following the abrasive regime of Di Canio.
The club made contact with the Uruguayan shortly after Di Canio's dismissal and then held talks with the manager, in which he is believed to have impressed club chiefs.
The former Chelsea and Tottenham midfielder is a free agent following his unedifying end at Brighton, which culminated in him being sacked while appearing live on television as a pundit.