Suarez, who joined Barcelona from Liverpool in 2014, leaves the club having won the Champions League, four La Liga titles and four Copa del Rey trophies. He scored 198 goals for the club in all competitions.
The Uruguayan was deemed surplus to requirements by new manager Ronald Koeman, who is keen on changing the old guard and rebuilding the squad, with 33-year-old midfielder Arturo Vidal also completing a permanent move to Inter Milan.
Suarez becomes the third striker in recent years to switch between the two La Liga clubs after David Villa was sold to Atletico in 2013 while Antoine Griezmann moved to Barca last year.
While Villa became an instant hit, scoring 13 goals in Atletico’s 2013-14 league title-winning campaign, Griezmann has yet to hit the same heights at Barca following his €120 million move.
Suarez had also been linked with Serie A side Juventus and took an Italian exam in an attempt to get an EU passport to be eligible to play as a European player as the Turin side’s non-EU player slots were already filled.