Bayern chairman Karl-Heinz Rummenigge said United have already agreed an undisclosed transfer fee, which German daily Bild report will be between 18 and 20 million euros ($20-22.31m, £12.9-14.3m), for the 30-year-old defensive midfielder, who has made 536 appearances for Bayern since 2002.
Schweinsteiger informed the German champions on Friday that he wanted a change of scenery and is expected to sign a three-year contract with the Red Devils.
“Bastian and I had a serious conversation on Friday. He told me he has been thinking about his career and wants to try something new,” said Rummenigge.
“He asked me to find a way and things between Manchester United and Bayern Munich have been clarified, we have agreed on a fair transfer fee.
“We have taken into account that Bastian is a very deserving player.
“We tried to convince him to stay with Bayern Munich, but I completely understand that after 17 years with us, he wants to experience something new.
“His nickname (with Bayern supporters) is ‘football God’ and it doesn’t happen very often that the fans shoot so high with a figure whom they identify.
“But at some point, a career has to end and now we’re required to manage his transition.”
The British media report Schweinsteiger will receive £140,000 per week in Manchester, £7.2m per season, which matches the 10 million euros he was receiving in Munich.
United confirmed the arrival of what is the first ever German player to join the club in a statement on their official website.
“Manchester United is delighted to announce it has reached agreement with Bayern Munich to sign midfielder Bastian Schweinsteiger, subject to a medical and personal terms,” the statement announced.
Rummenigge said Schweinsteiger had turned down the chance to take part in Saturday’s Bayern team presentation at the Allianz Arena to bid farewell.
The news was received with some boos and whistles from fans in the stadium, which grew quiet when Rummenigge told the 70,000-strong crowd: “it is what Basti wanted”.