The star forward arrived in Bavaria on a private jet from Majorca on Tuesday with his advisor Bjorn Bezemer and then went on to Barmherzige Bruder hospital to undergo his medical.
Mane has now put pen to paper on a three-year contract worth £250,000-a-week at the Allianz Arena, ending his six-year stay on Merseyside.
Bayern Munich have signed Sadio Mane from Liverpool and he has penned a three-year deal
Mane has put pen to paper on a three-year deal worth £250,000-a-week at the Allianz Arena
Mane posted with Bayern CEO Oliver Khan (L) and sporting director Hasan Salihamidžić (R)
Mane will work under new manager Julian Nagelsmann as Bayern chase another title
Speaking for the first time as a Bayern player, Mane said: ‘I’m very happy to finally be with FC Bayern in Munich.
‘We had a lot of talks and I felt the great interest of this big club from the start. So there was no doubt in my mind right from the start.
‘This is the right time for this challenge. I want to achieve a lot with this club.’
The Senegal star, who arrived at Anfield from Southampton in 2016 for £34m, played his last match for the Reds in the Champions League final defeat by Real Madrid.
Mane hinted before that match in Paris that his future may lie away from Anfield and then confirmed his intention to leave less than 24 hours after the full-time whistle.
In a farewell interview with Liverpool, Mane added: ‘Obviously it is strange – really, really strange – to no longer be a Liverpool player after six years spent at Anfield.
‘But of course I had a great time, an unbelievable time, and since my first day I really, really enjoyed training, playing, at Anfield especially and in front of these amazing supporters. Now it’s come to the end, so what can you say?
The Senegal star leaves Jurgen Klopp’s side after six successful years on Merseyside
‘I think whoever is leaving Liverpool, with those supporters you will always miss them because so far [they are] the best in the world and I have always said it.
‘I would love one day to come back to Anfield to say hi to them and of course to watch Liverpool playing because for me, I am going to be Liverpool’s No.1 fan – after the supporters!’.
When asked about the prospect of returning to Anfield in the Champions League, he said: ‘You know the Champions League and how the draw always goes on, it can happen for sure and if it happens it happens.
‘It is football and of course I have to come and I have to play. But like I said, Liverpool is Liverpool and we will see. We will see what is going to happen.’
Mane won the 2019 Champions League with Liverpool and the Premier League a year later
Mane won six major trophies during six years on Merseyside, claiming every major club honour, and scored a total of 120 goals in 269 games for the club.
This season, Mane scored 23 goals in 51 appearances in all competitions during a campaign where he also won the Africa Cup of Nations with his country.
His first trophy came in 2019 with the Champions League with the Premier League following a season later.
He completed his English trophy set by winning the League Cup and FA Cup this year, while he was also part of the side which won the 2019 UEFA Super Cup and 2019 FIFA Club World Cup.
Liverpool were initially reluctant to sell Mane, who has been instrumental in the transformation of Liverpool under Jurgen Klopp.
However in completing an £85m deal for Uruguay striker Darwin Nunez the Reds seem to have brought in a ready-made replacement.
Mane lifts the UEFA Super Cup in 2019 – a match against Chelsea in which he scored two goals
But with one year left on his current deal – a similar position Liverpool find themselves in with talismanic forward Mohamed Salah – they likely understood this would be their final chance to get a sizeable fee for the player.
Having already rejected two offers including what were considered unrealistic bonuses, Liverpool finally agreed a fee of £27.4m with an additional £5.1m based on appearances and £2.6m based on individual and team achievements.
Mane had said at the press day ahead of the Champions League final that he was going to give ‘a very good answer’ about his future after the game against Madrid but would not speak about it because his focus was on Paris.
Mane, though, did not make his way through the mixed zone in the early hours of Sunday morning after the Reds’ defeat and Liverpool officials were taken aback by reports that he has made his decision about what his next move will be.
Bayern boss Julian Nagelsmann has got his man, with Mane penning a three-year contract
Madrid, ironically, were always eager to sign Mane when Zinedine Zidane was manager but Liverpool always withstood interest and reward him with a new contract in 2019 but that deal was running out next June.
Barcelona have also been linked with Mane but the timing of Bayern’s links to Liverpool’s No 10 have always seemed significant and with doubts about whether Robert Lewandowski will remain in Bavaria, they believe the former Red Bull Salzburg forward would be an outstanding addition.
Pre-final, Liverpool legend Steven Gerrard urged Mane to stay at the club, saying: ‘[Mohamed] Salah has already said that he is going to be here next year, I know there is a bit of noise around Mane.
‘But why would you want to leave this Liverpool team? Because you know that they are going to be competitive in the business end of the season.’