Kane landed in Germany on Friday after the Bundesliga champions agreed a deal with Spurs.
The 30-year-old had one year left on his contract in North London but was intent on leaving his boyhood club to fulfill his trophy ambitions.
Kane is Tottenham's all-time record goalscorer with 280 goals in 435 games but has yet to win a trophy in his professional career.
In Bayern Munich, Kane is highly assured to get some silverware in his cabinet.
The Bavarians have been crowned champions of Germany in each of the last eleven seasons.
Kane has been registered in time to face RB Leipzig in the German Super Cup later on Saturday.
"I'm very happy to be a part of FC Bayern now," the England captain said on the club's official website.
"Bayern is one of the biggest clubs in the world, and I've always said that I want to compete and prove myself at the highest level during my career. This club is defined by its winning mentality -- it feels very good to be here."
Bayern finally have a replacement for Robert Lewandowski, who joined Barcelona last summer.
Kane's contract will last for four years and in his farewell message to Spurs, hinted he could return to the club later in his career.
He said: "I'm sad to be leaving the club I've spent nearly 20 years of my life at, from an 11-year-old boy to a 30-year-old man. There have been so many great moments and special memories that I will cherish forever.
"And mostly thank you to you the Tottenham fans. From the moment I've been playing I've been one of your own and I've given everything I possibly could to make you proud and give you as many special moments and memories that will hopefully last forever.
"I felt this was the time to leave. I didn't want to go into the season with a lot of unresolved future talk. I think it's important for the new manager and the players to concentrate on trying to get Tottenham to around the top of the table and fighting for trophies.
"I wish Ange and the boys all the very best of luck. Obviously I will be watching from a fan's point of view now and I really hope the team can be successful.
"This is a message to all you fans around the world, every single Tottenham fan has supported and been with me throughout my journey. Me and my family will cherish it forever. We'll never forget all the moments we've had together so thank you. I'll be watching the season.
"Good luck to Tottenham and the whole club. It's not a goodbye because you never know how things pan out in the future. Thank you and see you soon."
