Sources have confirmed to Goal that an agreement was reached after discussions between Barca president Josep Maria Bartomeu and Suarez's team.
Suarez will receive a settlement from Barcelona after the final year of his contract at Camp Nou is terminated.
That will free the 33-year-old to join Diego Simeone's men on a two-year contract, which will be worth €9 million (£8m/$11m) per season and include a number of incentives.
The Uruguayan is set to travel to Madrid to undergo a medical in the coming days and could even be in line to make his Atletico debut in Sunday's La Liga opener against Granada.
Suarez's move to Atletico appeared to be in some doubt after Bartomeu initially decided that he was unwilling to allow the striker to join one of his side's chief rivals.
However, the Blaugrana president has softened his stance and everything now appears in place for the forward to move to the Spanish capital.
Suarez has looked destined to leave Barcelona following the arrival of new head coach Ronald Koeman, who told the Uruguayan that he was not in his plans moving forward.
The veteran forward initially looked to be joining Juventus and even reached an agreement with the Serie A champions over a contract, subsequently travelling to Italy for a language exam in order to get a passport.
Juventus did eventually manage to sign a new striker, landing Alvaro Morata from Atletico Madrid on Tuesday on an initial 12-month loan deal, with the option for a second season and a permanent move for €45m (£40m/$52m).
Morata's departure will open up more minutes for Suarez, who leaves Barcelona having established himself as one of the club's all-time great strikers.
In his six seasons as a Barca player, the Uruguayan scored 198 goals and leaves as the club's third all-time top scorer, behind only Lionel Messi and Cesar.