This comes after he and Barca mutually agreed to terminate his contract.
Suarez, who is the Catalans’ third top scorer of all time, was informed by new Barcelona manager, Ronald Koeman, that he is surplus to requirements.
The 33-year-old had one year left on his current deal, but it has now been cut short by both parties.
Suarez has agreed on a two-year deal with Atletico, although they have to reduce their wage bill to accommodate him.
The Uruguayan was heavily linked with Juventus, but it appears to have fallen through, as there are delays in him obtaining an Italian passport.