A statement from Gareth Bale was published on Tottenham's official website:
I have had six very happy years at Tottenham but it's the right time to say goodbye.
We've had some special times together over the years and I've loved every minute of it.
I would like to thank everyone at the Club, the Chairman, Board, staff, coaches and players – and most of all the fantastic fans who I hope will understand this amazing career opportunity.
I am not sure there is ever a good time to leave a club where I felt settled and was playing the best football of my career to date. I know many players talk of their desire to join the club of their boyhood dreams, but I can honestly say, this is my dream come true.
I am well aware that I would not be at the level I am today were it not for firstly Southampton and then Spurs standing by me during some of the tougher times and affording me the environment and support they have.
Tottenham will always be in my heart and I’m sure that this season will be a successful one for them. I am now looking forward to the next exciting chapter in my life, playing football for Real Madrid.
More top news
A 21-gun salute was first sounded in the capital, Havana, as Castro's ashes were taken to the cemetery in eastern Cuba.
At least three children and 18 others - including members of the local police force - were among those who died.
The Foreign Secretary was unable to rule out the possibility of continuing to pay money into the EU when he spoke to Peston On Sunday.