The 38-year-old former Chelsea striker, who has 10 goals and six assists in 18 starts this season, missed Sunday's game but the team said in a statement that the two sides have since met and resolved their issues.
"Didier has accepted to assume the role that the head coach sees fit while contributing to the success of this club moving forward," Impact president Joey Saputo said.
"When he came to Montreal, Didier said he came here to win, and he still has the same objective."
Montreal had initially said Drogba, who was used off the bench in recent matches, was unavailable due to a stiff back but reports of discord were confirmed by the team after the match.
The Ivorian striker, who has been the subject of rumours of a move to Italy's Serie A, joined Montreal in mid-2015 after a stellar career in England with Premier League club Chelsea and wasted little time living up to expectations.
Yet Drogba has not started since a Sept. 24 loss as Montreal have relied more on Italian forward Matteo Mancosu, who has been impressive since being acquired in July on a year-long loan from Serie A club Bologna.
Without Drogba in the lineup on Sunday, Montreal clinched a playoff berth and can potentially host a knockout round match with a victory at New England Revolution when the regular season concludes on Sunday.
"Our main priority now is to focus on the last game of the season and the upcoming playoffs," said Saputo.
"With the players and the leadership that we have on this team, we are convinced that we can make a run at the MLS Cup."
(Reporting by Frank Pingue in Toronto; Editing by Ian Chadband)
