Speaking to De Telegraaf, Ryan Gravenberch said: "Manchester United is a very big and nice club. But I already had such a good feeling at Bayern Munich and I had them given my word.
"When the offer came from Bayern, I didn't have to think about it for long. Bayern are one of the biggest clubs around; players from all over the world want to play for this club.
"I'm coming to Munich to win lots of titles and Bayern are used to winning lots of titles. Anything is possible with this club, including winning the Champions League. The togetherness in this team is strong, which I like."
Earlier this month, Bayern officially confirmed the signing of the 20-year-old midfielder from Ajax for a fee of £21 million on a five-year contract.
Erik ten Hag was interested in bringing in the Dutchman to Old Trafford this summer but the Bundesliga giants have been leading the transfer race for months.