The Catalans' third top scorer of all time was told he was not wanted by new Barcelona coach Ronald Koeman and has been looking for a new club.
Suarez, 33, who has one year to run on his Barcelona contract, agreed a deal with the club to cut it short, reports said.
Mundo Deportivo said Suarez has fixed a contract with Atletico Madrid for two seasons, although the club will need to lighten their wage bill to accommodate the Uruguayan.
Reports in Italy say Juventus are in talks with Atletico to re-sign Spain striker Alvaro Morata. Suarez had been heavily linked with Juventus but coach Andrea Pirlo said it was unlikely he would come to Italy because of the difficulty in obtaining an EU passport.
The striker finished as Barca's second-highest scorer last season behind captain Lionel Messi and scored 198 goals in 283 games for Barca, after joining in 2014 from Liverpool.
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