Ribeiro moved to Wearside last October to support Black Cats boss Regis Le Bris and the rest of the club’s first-team coaching staff and players.
The 39-year-old was a key part of the Sunderland backroom team that helped mastermind the club’s promotion last season via the Championship play-offs.
However, the Black Cats have embarked on a major reorganisation this summer, which has led to Ribeiro agreeing to a mutual parting of the ways.
Luciano Vulcano was appointed as Sunderland’s new assistant head coach at the start of last month, with Isidre Ramon Madir being named as a new assistant coach and Neil Cutler joining the backroom staff as goalkeeping coach.
Sunderland sporting director, Kristjaan Speakman, said: “Following the recent restructure within our coaching team, we have been in regular dialogue with Pedro and agreed to mutually part ways.
“We thank him for his contribution to the club and for the role he played in our promotion-winning campaign. Everyone at the Academy of Light wishes him well in the next chapter of his career.”
