A Spurs statement said: "We have mutually agreed to the termination of Matt Doherty's contract to enable him to join another club.
"We should like to thank Matt for his service and wish him well for the future."
Doherty's departure was set to be a loan but that would have taken Tottenham up to nine players out on loan and FIFA's limit is eight.
The Republic of Ireland full-back made 71 appearances for Spurs after joining from Wolves in August 2020.
Atletico Madrid soon confirmed Doherty's move to the Spanish capital.
"Matt Doherty is a new Red & White player!" the LaLiga club tweeted.
"The Irish international joins our club for the rest of the season."
And then Tottenham announced the signing of Pedro Porro from Sporting Lisbon 10 minutes before the deadline.
The wing-back has signed on loan until the end of the season with an obligation to make the move permanent in the summer.
The 23-year-old, who signed for Manchester City in 2019, played twice against Spurs in the Champions League group stage.