Mane was unveiled as a Bayern player after signing a three-year contract with the Bundesliga champion, which has moved to strengthen its attack in the face of Robert Lewandowski's attempts to join Barcelona.
The Senegal international scored 90 Premier League goals for Liverpool in a highly successful six-year spell at the club, with Salah (118) the only Reds player to outscore him during that time.
Having also impressed for Southampton before making his move to Anfield, Mane hit at least 10 goals in all eight of his Premier League seasons – the most campaigns a player has played in the competition while reaching double figures each time.
After Jurgen Klopp branded Mane one of Liverpool's greatest ever players in the aftermath of his departure, strike partner Salah moved to thank him for his contribution to a successful era.
"It's been quite a ride!" Salah wrote on Twitter, alongside several images of the duo celebrating.
"Thank you for all the good times and I wish you all the best in your new adventure! You will be missed by all of us."
During his first press conference as a Bayern player, Mane said the decision to join Julian Nagelsmann's side was an easy one and he was already targeting competing for multiple trophies next season.
"When Bayern showed interest, I was intrigued and didn't have to think twice. I had other offers too, but I chose FC Bayern. They're the right club for me," he said.
"At Liverpool we fought for every title. It's the same at Bayern. When you play at Bayern you have to have the mentality to want to fight for every title.
"My whole life is a challenge – and I love challenges. We have the right team together, everyone [here] is made to win titles. We will try everything to win all titles.
"When you've spoken to the club and the coach, I can see how strong we are. I've followed the Bundesliga and the Champions League and there's no doubt that they're one of the best teams in the world."
Mane represents the first major addition made by Bayern in the transfer window, but chief executive Oliver Kahn hinted he will not be the last.
"The transfer window is still open for a very long time," Kahn said. "We're watching everything that happens. We weren't satisfied with the second half of the season.
"We know exactly where we need competition, where we need to set stimulus points in order to be successful."
Asked about the potential impact of Mane, Kahn said the dynamic forward can raise the level of the Bayern squad as it bids to win a first Champions League title since 2019-2020.
"We want to try to win the Champions League every year," he said. "But you don't win it by saying it, you have to put it into action on the pitch, but also those responsible have to create the conditions.
"He's a player who can lead the others. His presence can raise the level within a team. That's the quality that players like him have. So it's important to have top stars like him in our ranks."