Olise, who has a five-year contract with Bayern, scored 10 goals in 19 Premier League games last season — despite missing much of the year with injuries — and was crucial to a strong run for Palace toward the end of the campaign.

The long-awaited move makes Olise the second new signing to be confirmed since Bayern hired Vincent Kompany to coach the team, following the earlier arrival of Japanese defender Hiroki Ito from Stuttgart.

“Michael Olise is a player who can make the difference and attracted great interest with his style of play," Bayern board member for sport Max Eberl said in a statement.

"We want new impetus in our team, new energy, new ideas — that's what players like Michael Olise stand for. During the talks, he quickly signaled that he really wanted to join FC Bayern. We're very much looking forward to him. He will enrich our game.”

Olise, who was born in London but played for France at under-21 level, leaves Palace after making 90 appearances in three years.

“We are hugely proud of what Michael has achieved at Crystal Palace, a club where he has developed greatly as a player," Palace chairman Steve Parish said.

“We respect his desire to further test himself at the highest level of world football, and I would like to personally wish him the very best for his next adventure with Bayern Munich in Germany which I'm sure we will all follow closely.”

Bayern is trying to shake up its squad after losing out on the Bundesliga title to Bayer Leverkusen and finishing third under former coach Thomas Tuchel.

Bayern has been linked with a string of potential new signings, including defensive midfielder Joao Palhinha from Fulham, a year on from a failed move to sign him. What's less clear is which current Bayern players might be sold to make way for new arrivals as the rebuild project gathers pace.