The 30-year-old, who had a year remaining on his contract at Anfield, is set to rubber-stamp his departure on Wednesday in a deal worth an initial £27.5m.
Mane landed in Munich on Tuesday for a medical check-up and was seen sporting a Bayern shirt as he left the clinic. The club is expected to officially announce the deal imminently.
“My life has always been a challenge. When my adviser informed me of Bayern’s interest for the first time I was all flame and fire,” he told German newspaper Bild.
“I could instantly see me there. For me it was the right club at the right time. It is one of the world’s biggest club who always battles for all titles.
“For me the feeling was right when Bayern presented their plan. I saw myself in Bayern’s plan more than in any other.”
Mane leaves Anfield after 269 appearances, having scored 120 goals in all competitions, a stellar return that helped the club to the Champions League title in 2018-19 and the Premier League crown a season later.
The forward is set to become Bayern’s third signing of the close season, following the arrivals of Ajax duo Ryan Gravenberch and Noussair Mazrouai.
Bayern are desperate for his versatile attacking spark, with wingers Serge Gnabry and Leroy Sane having lacked consistency in the past season.
The Bavarians still won the German league for a 10th straight time but failed to get past the quarter-final stage in the Champions League.
Mane was among Liverpool’s stand-out performers last season, netting 23 times as Juergen Klopp’s side secured the domestic cup double and narrowly missed out on the league title to Manchester City.