Harry Kane completed his £100m move to Bayern Munich from Tottenham and made his debut on Saturday, coming off the bench in his side's 3-0 German Super Cup defeat to RB Leipzig.
"I'm very happy to be part of Bayern, one of the biggest clubs in the world and I've always said that I want to move and prove myself at the highest level in my career", said Kane, who signed a four-year contract.
"This club is defined by its winning mentality - it feels very good to be here."
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Kane: Right time to leave - but it's not goodbye
In a farewell message to Tottenham, Kane said it was the right time to leave the club - but added this may not be goodbye forever.
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."
How Kane's Friday unfolded
Tottenham's all-time top scorer was informed at around 3pm on Friday that his transfer to Bayern had been agreed and he could travel to Munich for his medical.
Kane's flight took off at 4.50pm UK time and landed at 6.10pm UK time at Oberpfaffenhofen airport just outside Munich.
The deal between Tottenham and Bayern for Kane will comprise an initial £86m fee, with add-ons taking the price close to £100m - which is a Bayern and Bundesliga record fee.
After Kane was told that a deal had been agreed between the clubs on Thursday, he decided to accept Bayern's offer.
Kane completed his medical and signed his Bayern contract at around 1am UK time on Saturday morning.
Levy: Kane forever in our history
Tottenham chairman Daniel Levy said: "We sought over a long period of time to engage Harry and his representatives in several forms of contract extension, both short and long term. Harry was clear, however, that he wanted a fresh challenge and would not be signing a new contract this summer. We have reluctantly, therefore, agreed to his transfer.
"We have seen a product of our academy system become one of the best players to ever pull on a Spurs shirt and become one of world football's elite strikers. It has been a truly remarkable journey.
"Harry's achievements and records say everything about the player, and throughout his 19 years at the club, Harry has been a model professional, on and off the pitch and an inspiration for young players who dream of following in his footsteps.
"I should like to thank Harry for everything he's done for us, all the memories, all the records - we wish him and his family all the best for the future. It goes without saying, he's always welcome back. He's a much loved and valued member of the Spurs family, forever in our history."
Tottenham's season-opening Premier League game is at Brentford on Sunday August 13, live on Sky Sports.
Kane scored 30 Premier League goals last season in a disappointing campaign for Spurs as they finished eighth to miss out on European football, while they remain without a trophy since 2008.
Kane scored 280 goals in 435 appearances at Spurs, having scored his first in December 2011.
With 213 goals in 320 Premier League games, he is currently 48 goals off breaking Alan Shearer's record as the highest scorer in Premier League history.
Watch Bayern Munich live on Sky Sports!
Bayern start their Bundesliga title defence at Werder Bremen, live on Sky Sports Action on August 18 - kick-off 7.30pm.
Bayern then face a home fixture against Augsburg, live on Sky Sports Football on August 27, kick-off 4.30pm.
Redknapp: Spurs should have done Kane deal earlier to give Ange time to adapt
Sky Sports' Jamie Redknapp on the Essential Football Podcast:
"I feel sorry for Ange Postecoglou because he is the person that's trying to get his team prepared for the start of the season. And you know, we're hours away from the start of the season and his star player is going to be leaving. I mean, this could have been done a couple of months ago, a month ago, to give him the best opportunity.
"It doesn't really feel that whoever's making these decisions - Daniel Levy - is thinking what's best for the team. A new manager in the door, you want to give him everything at his disposal to make sure that he's got a great chance of pushing, trying to get back into that top four.
"Yes, you might have got a little bit more money out of the deal, but that doesn't necessarily make it right for the team.
"It's a huge loss for the Spurs fans, you feel sorry for them that their hero is going to be leaving a day before the season starts. Harry Kane is irreplaceable."
'Bayern fans comparing Kane to Lewandowski - no concerns about throwing him straight in'
Sky Sports News reporter Paul Gilmour:
"Here in Munich, Bayern, and everyone associated with them - including some fans that we have spoken to - have been rejoicing at the fact they now have signed the England captain, one of the most elite goalscorers in world football. He's someone they are comparing to Robert Lewandowski; someone they think can make the same sort of impact Lewandowski did.
"Harry Kane had a long old day yesterday. He was waiting at the airport early in the morning, had to hold back and then eventually travelled and landed here in the evening. He went straight to a local hospital, had the first part of his medical, then went to the Bayern training ground, which is where we caught up with him and saw him waving at about 12.45am this morning.
"That was a sign that things had progressed, the medical was complete. It was shortly after that he signed the contract and he was a Bayern Munich player. He did the media stuff this morning, including an announcement video from the German champions.
"I think we're going to see Kane in action for Bayern Munich tonight. He has the chance to win a trophy on day one of his new job. He signed the contract at about 2am, his debut could come less than 24 hours after that. The last couple of days have probably been quite draining for all involved in the negotiations, but Kane has tried to keep himself ticking over and alert.
"We know he has been training as normal with Tottenham and is in good physical shape - he's the ultimate pro - so there are no concerns about throwing him in and he will wear the No 9 shirt.
"He has the potential to earn, we're told, in the region of £11m per year after tax - which is broken down into basic salary, games played and bonuses as well - across the four years of his contract."
'Kane is moving to Bayern to win the treble'
Sky Germany's Florian Plettenberg:
"It's difficult to describe this transfer in words. It's not just a transfer. It's getting Harry Kane, the superstar of the Premier League, the captain of the Three Lions, it would be a massive statement transfer for Bayern Munich, Germany and the Bundesliga.
"The mission for Kane is to win the Champions League with Bayern Munich and Thomas Tuchel, not the Bundesliga. The ambition is to win the treble and Kane is a treble transfer."
Bayern chief: Kane signing is something special
Bayern Munich executive board member Andreas Jung speaking exclusively to Sky Sports:
"I think it is the financial evolution of football. For us, it is the first time that we pay on that level for a player but we know that other teams who have investors, for them it is not a big issue to have a player for €100m. For us, it is something special.
"On the other hand, it shows that we are competitive with the others. We will have a team that, in every competition that we play, has the chance, the opportunity, to win that competition. Therefore, I think it is a good signing. A player like Harry Kane will, for sure, help us, in combination with the other players.
"So, everyone is now looking forward to when he is allowed to play.
"I think he is a top player. He scored the most goals at the 2018 World Cup and is every year a top scorer in England so there is no discussion about him as a football player."
Merse: Spurs are bottom half without Kane
Sky Sports' Paul Merson:
"Yes he's 30 years of age but I don't really pay attention to any of that. The way he plays, I think he can play until 35, 36 easily. He doesn't rely on pace, his brain is as good as anybody's.
"I'm still shocked here and I don't know why Manchester United didn't buy him. If they had, they would have got a good four or five years out of him and they would have won the Premier League.
"Will this Tottenham team get in the top four next season? I'd be shocked. So it's not like you're keeping him and definitely getting in the top four, so whatever we lose by selling him, you're making it back in the Champions League. That isn't going to be the case.
"Kane scored 30 goals last season and Spurs finished nowhere near. You feel sorry for Ange Postecoglou but you're talking about a team who might get in the top four if he stays, to a team who doesn't get in the top half if he leaves. They won't even get in the top half! They're 100 per cent a bottom-half team if he leaves.
"Who is going to get the goals? They finished eighth last season. I like James Maddison, he's a good player, but Leicester got relegated."