The 18-year-old Wales international was given permission to speak to the north London outfit over the weekend and the two clubs have confirmed that a deal has now been struck.
Gunter made his Bluebirds debut back in August 2006 in a Carling Cup tie against Barnet, while he made his full debut for his country in May this year in a friendly against New Zealand.
The teenager, who can play in either full-back position, has already made 33 appearances for the Championship club.
"We are delighted to announce that we have reached agreement with Cardiff City for the signing of Welsh international defender Chris Gunter," confirmed a statement from Spurs.
"The transfer will be completed upon the opening of the January transfer window."