The 20-year-old has joined the Bundesliga champions for a reported fee of €19million plus a further €6m in add-ons, signing a five-year deal.
He becomes the second Ajax player to sign for Bayern in recent weeks, with Moroccan full-back Noussair Mazraoui also moving to the Allianz Arena.
Gravenberch made 103 appearances in all competitions for Ajax, scoring 12 goals, having come through the club’s world-famous youth system.
He also played in all eight of Ajax’s Champions League games this season, making 376 passes at a completion rate of 88.8 per cent.
Gravenberch also took more shots at goal (four) than all but two of his team-mates, with only Antony (eight) and Mazraoui (five) attempting more.
Speaking to Bayern’s website after his signing was confirmed, Gravenberch said: “When the offer came from FC Bayern, I didn’t have to think about it for long. FC 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 FC 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 very strong, which I like.”
Bayern CEO Oliver Kahn added: “Ryan Gravenberch is a young, highly interesting player who lots of Europe’s top clubs would’ve liked to have signed.
“He’s chosen FC Bayern because he can develop at the highest level here. Players with his qualities are important for Bayern’s future path.”