Schweinsteiger looks set to complete his move to Old Trafford for a fee Sky sources understand to be around £14.4m with his medical due to take place on Sunday.
With both clubs confirming on Saturday that an agreement had been reached for the 30-year-old to leave after 17 years at Munich, his former team-mates were swift to express their regret over the proposed transfer.
“We have to simply respect and accept his decision. He’s looking for a new challenge, but for me it’s an absolute pity he is going, I have to say,” said Lahm.
Having made 536 appearances for Bayern since his debut in 2002 as an 18-year-old, Schweinsteiger has won all there is to win in Germany.
Bayern’s vice-captain collected his eighth Bundesliga winners medal last season and has lifted the German Cup seven times. He was also a key figure in the 2013 treble-winning side which won the Champions League, league and cup crowns.
Bayern’s Brazil international Rafinha added: “He’s a great player and there’s no need to talk about him as a footballer.
“He was a leader for us and everyone here is sad that he’s going, but I hope he has a lot of success at Manchester United.”
Bayern striker Robert Lewandowski echoed Rafinha’s sentiments by wishing his ex-team-mate “all the best”.
Despite his departure Munich will still be able to boast the likes of Spain stars Xabi Alonso, Thiago Alcantara and Javi Martinez in their central midfield.
They have also signed Brazil winger Douglas Costa and Germany U19 midfield talent Joshua Kimmich for next season.
Schweinsteiger’s national manager Joachim Low has backed him to be a success at Old Trafford.
“Basti is an absolute leader and world-class player who can put his stamp on any team, including of course Manchester United,” he told the German Football Association’s (DFB) official website.
“He knows Louis van Gaal, who wanted him unconditionally. I know from him that he still has big ambitions and goals.
“He will approach his new challenge in England like we all know him – with dedication and highly-motivated. For Bayern and the Bundesliga his departure is without question a loss.”