The 30-year-old signed a three-year deal with the Red Devils on Monday, and has revealed his desire to add to his eight Bundesliga titles, seven German Cups and his coveted World Cup crown.
"Everything is fine and I'm looking forward to giving my best for Manchester United and I'm really happy to be here,” he told MUTV.
"I'm here to win titles and that's what United is used to, too. I'm looking forward to playing in the jersey.”
Schweinsteiger has re-united with former Bayern Munich manager Louis van Gaal, yet insists his move was because of the club, and not the coach.
"I know Louis van Gaal, so coming here was a little bit easier, but it's not about him, it's more about the club, such a big club with tradition and, with this quality in the team, we can win titles next season,” he asserted.
"I'm looking forward to that moment in the jersey and to play for the team and the great supporters."
The Germany skipper, who has 111 caps for his country, scored 70 times in over 500 appearances for Bayern since his debut in November 2002.