The 30-year-old won the Champions League, Premier League, FA Cup, League Cup and Club World Cup titles during six years on Merseyside.
“My agent told me that there were also enquiries from other clubs, but for me, the feeling was right from the start when Bayern presented their plan with me,” Mané told German daily Bild.
“It was the right club at the right time.
“It is one of the biggest clubs in the world and the team are always fighting for all the titles.”
Mané added he wants to “do everything to make sure I win titles with my teammates”.
Bayern won a 10th straight Bundesliga title last season.
Mané, voted African footballer of the year in 2019, is a versatile attacker who has spent the majority of his career on the wing but can also play through the middle.
His arrival will ease the pain for Bayern if wantaway striker Robert Lewandowski leaves the club, while Serge Gnabry is also stalling over a contract extension.
“Sadio Mané is a global star, who underlines the appeal of Bayern and will increase the attractiveness of the Bundesliga as a whole,” said Bayern president Herbert Hainer.
“Fans come to the stadiums to see unique players like this.”
‘Top international star’
The signing of Mané takes some pressure off Bayern sporting director Hasan Salihamidzic after Lewandowski made it clear he would not extend his contract which expires next year.
Mané netted 120 goals in 269 games for Liverpool.
“In Sadio Mané, a top international star is coming to FC Bayern, who has left his mark on world football,” said Salihamidzic.
“We’re proud to have brought him to Munich.
“The fact that he’s joining FC Bayern shows that our club and he have big aims.”
Mané left Senegal at the age of 19 to join Metz and spent a season in France before joining RB Salzburg, where he learned German.
He switched to the Premier League when he joined Southampton in 2014 and moved to Liverpool two years later.
Mané played leading roles as Liverpool won the 2019 Champions League and ended their 30-year wait for the English league title in 2020.
“It is really strange to no longer be a Liverpool player but I had an unbelievable time,” he told Liverpool’s website. “I am going to be Liverpool’s number one fan forever.”
Mané, Senegal’s record goalscorer, was part of the team which won the Africa Cup of Nations in February, converting the winning penalty in the final shoot-out against Egypt.
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