Man United have reportedly paid between €18m and €20m for the German World Cup winner, who has signed a three-year contract.
Schweinsteiger and Bayern chairman Karl-Heinz Rummenigge agreed the transfer before the player went on holiday earlier this summer and the move was eventually confirmed on Thursday upon his return.
The 30-year-old has won everything there is to win with Bayern and the club has given him their blessing to make the switch.
United fans will be excited to hear about the signing as the team were crying out for a dominant presence in the middle of the park last term.
The Frenchman has been strongly linked with a move to Old Trafford in recent weeks but Louis van Gaal may decide that Schweinsteiger is enough as far as incomings are concerned.