The 25-year-old Morocco international has signed a contract until 2031, with the German champions paying a fee of €55m including bonuses.
Anthony Gordon, Bradley Barcola and Yan Diomande had all been linked with Bayern Munich in recent weeks, but it is Saibari who has completed the move to the Säbener Straße.
Sporting director Max Eberl said the club were delighted to land one of the standout attacking players at this World Cup.
"We are very pleased to have won Ismael Saibari, one of the most exciting attacking players at this World Cup, for FC Bayern.
"Such transfers don't happen in the moment but through forward-thinking work. It was decisive that we positioned ourselves early with him, because we knew of Ismael's abilities and were able to show him a concrete perspective with us from the start.
"Ismael Saibari will give our attacking play extra quality and unpredictability."
Saibari scored 19 goals and provided nine assists in 37 competitive matches for PSV last season.
He is also a regular for the Morocco national team and has featured at the World Cup in North America, scoring three goals in four appearances.
Sporting director Christoph Freund also praised the new signing.
"Ismael Saibari has won the Dutch title three times in a row with Eindhoven, has Champions League experience and is now showing at the highest level at the World Cup how valuable he can be for a team.
"He is versatile, intense, brave in his play, has exactly the hunger we want to see at FC Bayern and will do the team good with his goal threat and mentality. Fans come to the stadium for players like this."
Saibari said joining Bayern had been a childhood dream.
"Even as a child you dream of signing a contract with a club like FC Bayern — everyone knows it's one of the biggest clubs in the world."
"FC Bayern play for the biggest titles like the Champions League every year, and I want to win as many titles as possible here. The style of FC Bayern suits me, I can play my game here and I will work hard every day to help the team."
"Coach Vincent Kompany played a big role in my decision — I'm really looking forward to working with him."