With Spurs set to bring in Pedro Porro from Sporting CP, Djed Spence was sent on loan to Ligue 1 side Rennes and fellow wing-back Doherty also left north London on Wednesday (AEDT).
The Republic of Ireland defender was reportedly set to join Diego Simeone's side on loan but has signed a contract until the end of the season.
Spurs released a statement to confirm Doherty's contract had been terminated to "enable him to join another club".
The 31 year-old former Wolves defender follows in the footsteps of Kieran Trippier, who swapped Spurs for Atletico in 2019 and lifted the LaLiga title with the Rojiblancos in the 2020-21 season.
As Doherty heads to Madrid, Atletico defender Felipe goes the other way to England after completing a move to Nottingham Forest.
The 33 year-old started just two LaLiga games for Simeone's side this season, seemingly falling out of favour behind Mario Hermoso and Jose Gimenez.
Felipe's Atletico contract was due to expire in June before he signed a deal running until 2024 for Forest, where he looks forward to a new challenge in the Premier League.
"It was a dream of mine to play in the Premier League and I'm really excited to be part of this wonderful, fast-growing club," he told the club's official website.
"You can see it's a club looking to really grow. It's a big challenge for me and I made a clear decision to be part of the history here and grow with the club."