Sources have told ESPN the fee for Memphis could rise to over €4 million.
"Memphis Depay is a new Atletico de Madrid player following the agreement reached with FC Barcelona for the transfer of the Dutch striker to our club, signing for the remainder of the season and two more seasons," said a club statement.
The Netherlands international's contract at Barca was due to expire in June and he had played a minimal role at Camp Nou this season, starting just two league games.
Atletico are looking to strengthen their forward line after they allowed Joao Felix to join Chelsea on loan and Matheus Cunha moved to Wolves, leaving them relying on Alvaro Morata, Antoine Griezmann and Angel Correa in attack.
Diego Simeone's side are having a difficult season, eliminated from the Champions League at the group stage and battling to finish in the LaLiga top four, although they qualified for the Copa del Rey quarterfinals on Wednesday with a 2-0 win at Levante.
Speaking at a news conference on Friday, Simeone said: "A player that has a lot of enthusiasm has arrived. He is eager to rediscover his best form.
"We are working so that we can find the player he was at Lyon, where he showed his physical strength and his abilities. We will work with him to help him reach his best form and that he, in return, can give us what we want from him.
"He can play as a forward or as a second striker. I see him similar to [former Atletico forward Diego] Costa, who started out as a striker but ended up forward because of his explosive play, his strength and his good finish.. Memphis has proved, especially in France, and in his first year at Barca that he has good numbers."
Memphis, 28, had missed training with Barcelona on Wednesday as the move neared completion.
Sources told ESPN the initial fee would be €3m, with just over €1m potentially due in variables.
He began as a regular with then coach Ronald Koeman -- scoring 12 league goals in his first season -- but has featured less under Xavi, who has preferred to pick Robert Lewandowski, Ansu Fati, Ousmane Dembele, Raphinha and Ferran Torres this campaign.
ESPN's Adriana Garcia also contributed to this report.