The 61-year-old had been working with the Scottish Football Association and formerly he was United's reserve coach from 2002 to 2005.
During his previous spell at Manchester United, he won the Manchester Senior Club, the Premier Reserve League North and the Premier Reserve League Championship in 2005.
Sbragia told the club's official website: "I couldn't be happier to be back at Manchester United. It's an exciting time for the club, with a new structure for the Academy and a relatively new set of coaches and management team."
He has been without a job since he resigned from his job as Scotland Under-21 boss in February. Sbragia has also spent some time with Bolton and took charge of Sunderland's first team.