The 30-year-old landed in Munich on Tuesday morning to undergo his medical to seal his departure from Liverpool after six years at the club.
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Last week, ESPN reported that the Bundesliga champions reached an agreement to sign Mane from Liverpool in a deal worth up to €41 million.
Liverpool will receive €32m up front for the forward, with a further €6m due when he meets a specified appearance clause and an additional €3m based on individual and team achievements.
Mane was spotted wearing a Bayern training jersey on Tuesday as he sets his sights on a new journey in the Bundesliga.
Mane could make his debut for Bayern when they face RB Leipzig in the season-opener DFL Supercup on July 30.
The forward will leave as a Liverpool legend after helping the team to Champions League success in 2019 and their first Premier League title in 2020.
He also won the Club World Cup (2019), FA Cup (2022) and Carabao Cup (2022) as he scored 120 goals in 269 games in all competitions during his time at Anfield.