During his three seasons at Palace, the 22-year-old forward for France Under-21, who was born in England, made 90 appearances in all competitions.
Olise signed a five-year contract after joining the Eagles for £8 million in July 2021 from Reading.
Earlier this summer, Olise attracted interest from Chelsea and Newcastle United, but he decided to travel to Germany and work under new Bayern manager Vincent Kompany.
“I’m very happy to now be playing for such a big club – it’s a great challenge and that’s exactly what I was looking for,” Olise remarked.
“I want to show my mettle at this level and contribute to our team’s championship run.”
In 19 Premier League games, Olise netted 10 goals, helping Palace place 10th in the standings the previous year.
He’s been added to the France Olympic team, which will begin in Paris later this month.
Eagles chairman Steve Parish said, “We are incredibly proud of what Michael has accomplished at Crystal Palace, a club where he has greatly developed as a player.”
