“Bastian wants to do something new at the end of his career,” he told a news conference.
“The colleague from Manchester United got in touch with me. We have agreed on a transfer.
“I regret that because Bastian was an extremely deserving player for us. He has done great things. I can only wish all the best to Bastian. It will be an interesting task for him.”
United confirmed they had reached an agreement to sign the 30-year-old subject to a medical and personal terms.
A World Cup-winner with Germany in Brazil last year, Schweinsteiger came through the youth ranks at Bayern and has spent 13 seasons with the Bavarians, winning the Bundesliga title eight times.
During a glittering career, Schweinsteiger, who made 536 appearances for the club since his debut in 2002, also won seven German Cups and the Champions League in 2013.
Germany captain Schweinsteiger has been a mainstay in their midfield since his international debut in 2004, scoring 23 goals in 111 appearances, and is their fifth-highest capped player.
“(Schweinsteiger) is an absolute leader and world-class player, who can make his mark on any team,” Germany coach Joachim Low told their official twitter feed after the announcement.
Schweinsteiger’s arrival is a statement of intent by United who are bidding to re-establish themselves after seventh- and fourth-place finishes in their previous two league campaigns.
They spent heavily during the last close-season bringing in the likes of Angel Di Maria, Radamel Falcao, on loan, and Luke Shaw but were still overly reliant on 33-year-old midfield lynchpin Michael Carrick.
Schweinsteiger cites United great Eric Cantona as one of his heroes and plays in the same mould. He is likely to assume much of the midfield responsibilities at Old Trafford.
He will be the first German to play for United and their second signing of the close-season following the arrival of Netherlands winger Memphis Depay from PSV Eindhoven for a fee of about 30 million euros (21.5 million pounds).
United manager Louis van Gaal confirmed on Friday that Italian defender Matteo Darmian will have a medical at the club ahead of a proposed transfer from Serie A side Torino.
(Writing by Tom Hayward, editing by Ken Ferris)