Frank and his team has left Brentford to succeed Ange Postecoglou after his dismissal a week ago.
The Dane has signed a deal to 2028 with Spurs after compensation was agreed with Brentford.
Tottenham announced on Thursday: "We are delighted to announce the appointment of Thomas Frank as our new Head Coach on a contract that runs until 2028.
"Thomas has extensive experience in English football having joined Brentford in 2016 - since becoming one of the longest-serving current managers in the Premier League. During his time at Brentford he transformed the Club, moving them up from the Championship to an established Premier League side, consistently and significantly outperforming expectations for an extended period of time.
"In Thomas we are appointing one of the most progressive and innovative head coaches within the game. He has a proven track record in player and squad development and we look forward to him leading the team as we prepare for the season ahead.
"Thomas will be joined from Brentford by Justin Cochrane (First Team Assistant Coach), Chris Haslam (Head of Performance & First Team Assistant Coach) and Joe Newton (First Team Coach Analyst), with Andreas Georgson (First Team Assistant Coach) arriving from Manchester United."