Suarez was deemed surplus to requirements at the Camp Nou after new Barcelona manager Ronald Koeman took over from Quique Setien last month.
The 33-year-old Uruguayan international spent six seasons with Barcelona after joining from Liverpool in the summer of 2014.
Suarez won four La Liga titles, the 2015 UEFA Champions League and four Copa del Reys among other honours during his time in Catalonia.
His goal tally of 198 in 283 games for Barcelona puts him third on the list of the club’s all-time top scorers, behind only Cesar and Lionel Messi.
"FC Barcelona and Atletico Madrid have reached an agreement for the transfer of the player Luis Suárez. The Madrid club will pay FC Barcelona 6 million euros in variables," the Blaugrana announced in a statement.
"FC Barcelona would like to publicly express their gratitude to Luis Suarez for his commitment and dedication and wishes him all the best for the future."
Suarez’s arrival at Atletico Madrid will help augment the loss of Alvaro Morata, who has joined Juventus on a season-long loan deal.
Suarez could make his debut for Diego Simeone’s men this weekend when they host Granada at the Wanda Metropolitano Stadium in their opening La Liga game.