The Catalan club confirmed on Wednesday that the Uruguay striker will leave for the Spanish capital and will hold a farewell press conference on Thursday.
Suarez, 33, joins Atletico on a free transfer, although Barca could make up to €6 million on the move based on a number of performance-related variables.
The deal is expected to be for two years, with Atletico stating the deal is subject to a medical examination.
The Rojiblancos, like Barca, are in a period of financial uncertainty due to the coronavirus pandemic and needed to make room on their wage bill before signing new players.
The move draws parallels with David Villa's switch from Barca to Atletico in 2013. With Villa up front, Simeone's side won the La Liga title and reached the Champions League final, knocking Barca out along the way.
Suarez, who recently became the third-highest scorer in Barca's history with 198 goals, was told he was surplus to requirements by new coach Ronald Koeman last month.
That prompted the player's legal team to begin talks with the Catalan club over the early termination of his contract, which had one year left to run.
An agreement was eventually brokered on Monday which would see Suarez give up a percentage of what he was owed in exchange for being allowed to leave for free.
However, when it emerged he planned to join Atletico, Barca, who didn't want to strengthen a direct rival for free, backtracked on the original agreement.
Sources told ESPN that Suarez was furious at the club's U-turn, but a meeting between Barca president Josep Maria Bartomeu and the player's lawyers on Tuesday helped get things back on track.
Suarez had previously rejected the chance to join Inter Miami, who offered him the chance to become the highest-ever paid player in Major League Soccer with a deal worth around €8m annually.
He also looked close to joining Juventus at one time. To move to the Serie A champions, though, he needed to obtain Italian citizenship, which meant passing a language exam in Perugia last week.
That language test has since become the centre of a scandal, with confirmation from the Italian authorities on Tuesday that it's under investigation from prosecutors amid irregularities.
Suarez himself is not under investigation.
Atletico had always been waiting in the wings and Suarez was always keen to remain in Europe. Sources say he was especially excited at the prospect of working under coach Simeone.
The striker leaves Barcelona six years after signing from Liverpool for €75m. During his time at Camp Nou, he won 14 trophies, including four La Liga titles and one Champions League.
Suarez's final game for Barca was the 8-2 defeat to Bayern Munich, which prompted the Catalan club to begin a major overhaul of the squad. Suarez joins Ivan Rakitic, Arturo Vidal and Nelson Semedo who have all exited the Camp Nou this summer.