L'Equipe says the Swede has settled on a contract with Galaxy, with negotiations having been ongoing for the past three weeks.
The only uncertainty now is whether Ibrahimovic sees out his deal with United and joins Galaxy in the summer, or chooses to move to Los Angeles immediately.
The centre-forward has returned to training at United this week after suffering a minor setback in his recovery from April knee surgery.
Just yesterday, United boss Jose Mourinho declared: "Zlatan is in his final year on the contract. If it's true and Zlatan wants a future in another country, then we're here to help and create the conditions for him to leave, we do not want to make his life difficult."