Osuna has not pitched since May 6, two days before he was put on administrative leave when he was charged with one count of assault in Toronto.
Suggesting that a negotiation was involved, Major League Baseball commissioner Rob Manfred said on Friday that Osuna has "accepted a suspension without pay" through August 4.
The league's announcement said Osuna "accepted" the length of the suspension after MLB completed its investigation of the incident under its Joint Domestic Violence, Sexual Assault and Child Abuse Policy.
Major League Baseball suspended Toronto Blue Jays closer Roberto Osuna for 75 games following his arrest in May for a charge of assault, MLB Communications announced Friday. "Having reviewed all of the available evidence, I have concluded that Mr. Osuna violated the policy and should be subject to discipline in the form of an unpaid suspension".
The Blue Jays said in a statement that they "support the decision by the Commissioner's Office".
"I don't have much of a reaction other than you take what Major League Baseball does and trust that and live with that and let it go through its course, " Blue Jays manager John Gibbons said before Friday night's road game against the Los Angeles Angels.
Osuna, 23, has a 2.87 ERA with 104 saves in his career (parts of four seasons).
Osuna's next court date is scheduled for July 9 where his lawyer has said the native of Mexico will plead not guilty.
As a result, Osuna will forfeit $2.54 million of his $5.3 million salary. It allows the league to discipline a player for a domestic violence incident regardless of whether there are charges or a trial.
Osuna will now participate in a disciplinary treatment program in response to his actions.