Sadio Mane has completed a £35m move from Liverpool to Bayern Munich on a three-year contract.
The Reds will receive 32m euros (£27.4m) with an additional 6m euros based on appearances, plus 3m euros for individual and team achievements.
Liverpool turned down two bids from Bayern before agreeing a fee for the Senegal forward, who was under contract until next summer.
“This is the right time for this challenge,” said the 30-year-old.
“I felt the great interest of this big club from the start so there was no doubt in my mind.”
Mane joined Liverpool for 34million euros from Southampton in June 2016 and scored 120 goals in 269 games, finishing last season with 23 goals in all competitions.
“Sadio Mane is a world star who underscores the appeal of FC Bayern and increases the attractiveness of the entire Bundesliga,” said Bayern president Herbert Hainer. “It is for such unique footballers that the fans come to the stadiums.”
Mane helped Liverpool win the Champions League and the Premier League, and in February scored the winning penalty as Senegal won the Africa Cup of Nations for the first time.
“With his outstanding performances and his great successes at the highest international level over many years, there are very few players like him in the world,” added Bayern’s chief executive Oliver Kahn.
“We’re sure that Sadio Mane will delight our fans in the coming years with his spectacular style of play. He’s ambitious and eager to win more titles. This package is very strong. With players like him at FC Bayern, all the biggest goals are possible.”
Last week Liverpool confirmed the signing of Uruguay forward Darwin Nunez from Benfica for an initial £64m.
In a farewell interview for the Liverpool website, Mane said: “It is really strange to no longer be a Liverpool player but I had an unbelievable time. I am going to be Liverpool’s number one fan forever.”