The 30-year-old is closing on a move to Old Trafford with his medical taking place on Sunday and he took to Twitter to thank the Bayern fans over his 17-year association with the club, stating he wanted to “gain experience at a new club”.
He tweeted: “One last dream in my career come true. I am excited about the next chapter in my life with Man Utd.”
Schweinsteiger, part of the German World Cup winning team last year in Brazil, said in his video: “Hi dear Bayern fans, and the South Stand in Munich. I know that has been a lot of speculation about my future in recent weeks and months and I just wanted to thank you for the fantastic time we spent together.
“It started in the Olympiastadion and continued into the Allianz Arena. It was a really fantastic time and we experienced some great moments with 15 national titles, including the historic treble and other highlights.
“We are always going to have a bond and I will keep you in my heart forever. I also want to thank all the employees at the Sabener Strasse (training ground) for the great time we had together – unfortunately I can’t name everybody, but thanks for everybody, you helped me a great deal.
“I hope you, dear fans, understand that I have chosen this path now. I think it’s a great challenge and I’m looking forward to it, although I will never forget you.
“I will always hold you here [in my heart] and I hope we see each other again soon. Yours, Basti.”
In a written statement, he added: “The decision was very hard to make because you and FCB have and always will be an extremely important part of my life.
“Nevertheless, I would like to again gain experience at a new club. My destination is Manchester United. I hope you understand my decision. No one can take away the incredible journey we had together. #MiaSanMia.”
Schweinsteiger, who will become the first German to play for United, will leave behind a sizable gap in Bayern’s squad by leaving the Allianz Arena.
He has been on the Bavarian club’s books for 17 years and won eight Bundesliga titles, seven DFB-Pokals and the Champions League with Bayern among other successes.
Forward Thomas Muller, who has also been linked with a move to United, added: “It’s strange that Basti’s gone. He’s done sensationally for this club. He’s not going to be forgotten in a rush. I wish him a lot of luck. This is how things work in football.”
Meanwhile, former Manchester United captain Bryan Robson described Schweinsteiger as “top drawer” and a “true leader of men” who can drive the Red Devils back to the top.
Robson, 58, told The Sun: “Schweinsteiger is the kind of player and personality United have been short of.
“There is Michael Carrick, of course, who has that same experience and knowledge. When he was not playing last season, we saw that United were not the same team.
“Schweinsteiger is absolutely top drawer and his record and reputation speak for themselves. He is the kind of player that can lead United back to the very top.”