The former Chelsea midfielder returns to the Premier League on a five-and-a-half-year deal after an 18-month spell in Spain.
Spurs are expected to pay over £34 million for Gallagher, who has been a long-standing target of the club across several transfer windows.
"I'm so happy and excited to be here, taking the next step in my career at an amazing club," Gallagher said.
"I wanted to be a Spurs player and thankfully the club felt the same. It was very easy, it happened very quickly and I'm ready to get on the pitch.
"I know how great the fans are, I’m really happy to be a part of it here and want to create special moments and memories together."
Gallagher appeared to have been Villa-bound and Unai Emery's side had been closing in on a loan deal with an obligation to buy before Tottenham swooped.
Spurs have been forced into the midfielder market after learning Rodrigo Bentancur will be sidelined for three months with a hamstring injury.
Gallagher joined Atletico in August 2024 and made 77 appearances, scoring seven goals, although he has made just four starts in La Liga this season.
The move will likely come with an eye on making England's World Cup squad this summer, having been omitted from Thomas Tuchel's previous selection.
Gallagher has 22 caps to his name, with his last outing coming in the 3-1 defeat to Senegal over the summer.