The Crystal Palace talisman had long been a top target for the Blues and the Red Devils but snubbed interest in the pair as well as Newcastle United.
Chelsea thought they had signed Olise last summer but he instead penned a new deal at Selhurst Park which included a new release clause.
Bayern activated it last month, with the Frenchman keen to join the Bundesliga giants to fulfil his dream of playing in the Champions League, something rival bidders could not offer.
Speaking out after signing a five-year deal at Munich, Olise said: ‘The talks with FC Bayern were very positive, and 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. I want to prove myself at this level and play my part in ensuring that we win as many titles as possible with our team in the coming years.’
Olise joined Palace from Reading for just £9m in 2021 and quickly established himself as one of the Premier League’s best young talents.
Despite several big injury issues, the 22-year-old scored 10 goals and made six assists in just 19 appearances, helping fire Oliver Glasner’s side to a 10th place finish.
The fee makes him the Eagles’ record sale, surpassing the £45m United paid for Aaron Wan-Bissaka back in 2019.
‘We are hugely proud of what Michael has achieved at Crystal Palace, a club where he has developed greatly as a player,’ club 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.’
Olise won’t link up with Bayern straight away however, having been picked by Thierry Henry for France’s Olympics team alongside now former Palace teammate Jean-Philippe Mateta.
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