The 38-year-old former Chelsea and Ivory Coast star had stunned the club last weekend after demanding to be left out of the match-day squad upon discovering her would start on the bench.
The uproar left Drogba facing an uncertain future with Montreal as the club look towards the Major League Soccer postseason.
However Impact President Saputo said in a statement on Tuesday that the situation with the veteran striker had now been resolved.
“We met with Didier. The situation has been resolved to the club’s satisfaction,” Saputo said.
“Didier has accepted to assume the role that the head coach sees fit while contributing to the success of this club moving forward.
“When he came to Montreal, Didier said he came here to win, and he still has the same objective.
“Our main priority now is to focus on the last game of the season and the upcoming playoffs.”
The controversy is just the latest glitch in a turbulent second season in the MLS for Drogba, who was linked to a return to Chelsea in a coaching role last December.
Impact initially denied the story but then admitted they had been in contact with Chelsea amid reports that Drogba was considering announcing his retirement in order to escape the second year of his contract with Montreal to force a move back to Stamford Bridge.
Drogba denied the claim and eventually reported back for duty with the Impact.
Although he has scored 10 goals and contributed six assists this season, controversy has continued to follow him, with the player involved in a spat with New York Red Bulls fans last month.
The problems have led to mounting calls amongst fans for Drogba to be let go, with critics noting that the team’s record this season has been better when he has not played.