Schweinsteiger played nearly two seasons at Bayern Munich with Louis van Gaal as his manager before the Dutchman left at the end of the 2011 season – and he is happy to be reunited with the 63-year-old.
He said: “We know each other well. We had a great time there. It was very good for my development. We won titles.
“Of course it’s a new stage in my life now. I want to win titles. That’s easy and what I’m used to. That’s the goal for next year’s team. I will give my best to be successful.”
In April 2010, Van Gaal’s Bayern Munich visited Old Trafford for a Champions League semi-final second leg, holding a 2-1 advantage from the first leg in Germany.
United raced into a 3-0 half-time lead, but second-half goals from Arjen Robben and Ivica Olic silenced the Old Trafford crowd and took Bayern through to the final on aggregate.
But it was the response of the United supporters on the final whistle that impressed the Germany international.
He said: “I am here with Manchester United because it is a big club and I am looking forward to playing at the great stadium. The supporters are so important.
“I remember when I was there in a Champions League match when we lost 3-2 but we progressed to the final and the supporters were very respectful and gave us applause after the match. I am looking forward to playing in that great stadium.”
Morgan Schneiderlin has also been brought in by United after spending seven years at Southampton where he tasted life in League One before progressing to the Premier League.
He said: “It’s the best thing that happened to me. When I came to England every manager told me I was good but I had to toughen my play. There was no better place to learn that than in League One. Every game is a battle but I was able to improve.
“Today is the next step in my career. Of course it is more demanding, there is more pressure playing for Manchester United, but I cannot wait to continue my adventure and play for this side. When I learned Manchester United was interested there was no other choice.”
Both players could make their Manchester United debut in the first match of the pre-season tour against Mexico’s Club America on Friday night in Seattle.