The 17-year-old left-back became the youngest scorer in Welsh international history, earlier this season.
Bale said: “I am just excited to be coming to a big club, a massive club like Tottenham. I want to play in the Premiership, Tottenham is a club pushing forward and I want to be part of its future.”
Sporting Director Damien Comolli added: “We have been following Gareth for a long time now and have been very tenacious, so we are absolutely delighted to get him here. He is a player of great quality and, as we always say, our aim in each window is to improve the quality of the squad.
“Gareth has great physical attributes, he is tall, good in the air and has a fantastic left foot. He is very good on set pieces, he is clever on the ball and his passing selection is excellent.
“He has the ideal combination to become a top, top player and he is only 17.”