The 59-year-old is a former manager of Sunderland, while also holding coaching roles at Manchester United and Bolton.
The Scottish FA have promoted Sbragia from his position as coach of the under-19s, and he will be assisted by Donald Park who will continue in his role as head of coach education at the national association.
Sbragia said in a statement on the Scottish FA website: “I am very proud to have been offered the position of Scotland Under-21 head coach.
“I am acutely aware of the importance of the job in what for many young professionals should be the final stage before entering the full international team.
“The primary responsibility is to help prepare players to make that leap to Gordon Strachan’s ‘A’ squad but it is also important that we work hard to ensure we are ready to make an impact in the forthcoming European Championship qualifiers which start in September.”
Scotland start their European Under-21 Championship qualification campaign away to Northern Ireland on September 5, before hosting France and Iceland at Pittodrie on October 10 and 13.”
New performance director Brian McClair, who worked with Sbragia at Old Trafford, added: “Ricky has built up a wealth of knowledge and experience at the highest levels of coaching and the under-21s will now benefit greatly from that.
“I am also pleased to confirm Scot Gemmill as coach of our under-19 squad. I believe there should be a fluidity to our coaching structure (Gemmill formerly coached the under-17s).
“Having set out to speak to as many people in the game as possible during my first weeks in the job, I have been greatly encouraged by the enthusiasm and sense of common purpose shared by our member clubs to make the national game better. I am confident that these appointments will be a positive step in that direction.”