Schneiderlin’s move came shortly after United also confirmed the signing of World Cup winner Bastian Schweinsteiger from Bayern Munich.
Schweinsteiger, who has won 111 caps for his country, and Schneiderlin will join the rest of their new United team-mates who fly out for a pre-season tour of the United States on Monday afternoon.
United are believed to have paid Southampton £25million for the 25-year-old, who was believed to be interesting Arsenal boss Arsene Wenger.
Schneiderlin said: “Once I learned United were interested in me, it was a very easy decision to make.”
United boss Louis Van Gaal added: “Morgan is a very talented player with great energy and ability. His skills will complement the players that we already have and I am very pleased that we have been able to complete this deal before the tour to the United States.
“That training camp will be very important in our preparations for the new season and gives Morgan and the other players a chance to show our fans what they can achieve together.”