The suspension, announced by commissioner Rob Manfred, is without pay and covers 82 games, retroactive to April 30.
Olivera was arrested April 13 at a hotel outside Washington, D.C., charged with assault and battery of a woman and he was immediately placed on leave.
Agreeing with the police report filed in Arlington, Va., Manfred's office finished an investigation that concluded Olivera was responsible for visible bruises on the woman's body. A police spokeswoman said at the time that Olivera and the woman were acquainted.
Losing the 31-year-old Olivera was a big blow to the Braves, who have the second-worst record in the majors and rank last in homers, RBI and runs scored.
The Braves still owe Olivera over $28 million through a $47 million contract that runs through 2020. The Dodgers are paying the remainder.
Manfred's office said that Olivera will be allowed to participate in extended spring training activities during the suspension, followed by a rehab assignment beginning no sooner than July 15.
Olivera is the third player penalized under Major League Baseball's new domestic violence policy. Like Yankees closer Aroldis Chapman and Colorado shortstop Jose Reyes, Olivera agreed not to appeal his suspension.
A statement from Manfred's office said players suspended under baseball's joint domestic violence, sexual assault and child battery must participate "in a confidential and comprehensive evaluation and treatment program supervised by the joint policy board."
The Braves said in a statement that they fully support the decision, adding they "will have no further comment on the matter at this time."
In their first season last year under front office executives John Hart and John Coppolella, the Braves projected Olivera as their power-hitting third baseman of the future.
Olivera, a Cuban defector, made his major league debut Sept. 1 and hit .253 with two homers and 11 RBI in 24 games. Atlanta moved him to left field in spring training. In six games, he hit .211 with no homers and two RBI.