In return, Toronto got allocation money to help pay down some wages inside its salary cap.
On Monday, Toronto general manager Tim Bezbatchenko hinted at some future transactions by saying teams can always make moves if they're willing to make tough choices.
"And this is a tough choice for us," Bezbatchenko said Tuesday.
"We needed to make space and we thought this would strengthen our club," he added.
With a listed salary of US$251,666 last season, the speedy Oduro was a big-ticket item.
Toronto is also well-stocked in the midfield with designated players Michael Bradley and Sebastian Giovinco (who is currently slated to arrive in July), along with Jackson, Jonathan Osorio, Collen Warner, Marco Delgado, Daniel Lovitz and Warren Creavalle and homegrown players Manny Aparicio, Jay Champion and Chris Mannella.
The options are also deep up front with Jozy Altidore, Luke Moore, Robbie Findley, Bright Dike and Jordan Hamilton, with Giovinco also able to play as a withdrawn striker. Gilberto, meanwhile, is an unused asset back in Brazil while Toronto sorts out its designated player overflow.
Bezbatchenko said there could be more departures — to facilitate more moves.
"It is possible ... there's a couple of players we're looking at now."
Toronto traded midfielder Kyle Bekker to FC Dallas last week for allocation money, helping pave the way to acquire Polish international defender Damien Perquis and American defender Eriq Zavaleta.
Montreal becomes Oduro's seventh MLS stop following stints in Dallas, New York, Houston, Chicago, Columbus and Toronto.
"No condition is permanent as they say. Thanks #TFC for ur support. Had a blast. On to the next one. Hope I make it home #IMFC," Oduro tweeted Tuesday.
Known for his colourful mohawk hairstyle, Oduro will continue to push the hair envelope in Quebec, it seems.
"Time for a new barber in Montreal. Who's the best in town?#IMFC," he tweeted.
Oduro was ranked the fifth-fastest player in the world, according to the FIFA 15 video game ratings. He has 48 goals and 26 assists in 252 career regular-season appearances.
"This move allows us to add quality depth to our striker position, as we identified in our plan," Impact technical director Adam Braz said in a statement. "Dominic is an experienced player who has scored in our league and adds a different profile to our attacking options."
Bezbatchenko agreed that Oduro, with the right minutes and the right system, could score 10 to 15 goals a season. But that was not likely to happen in Toronto's current setup.
Oduro came to Toronto in a June 2014 deal that sent Spanish midfielder Alvaro Rey to Columbus. Because of the mid-season trade, Oduro managed to play in 35 games last season, one more than the regular season schedule for a team.
The Montreal deal comes one day after Oduro expressed his excitement at being back in camp.
"I'm really hungry right now," he said Monday. "This off-season I just missed playing soccer."
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