The veteran Côte d'Ivoire and former Chelsea icon addressed a crowd of fans at Montreal's Saputo Stadium, a day after jetting into the Canadian city after wrapping up his MLS move earlier this week.
"I am a man of challenges and there is a beautiful one before me," Drogba said alongside Impact President Joey Saputo.
"I'm proud that he decided to pursue his career here, and his arrival will be beneficial at all levels, both on and off the pitch," Saputo added. "I just want to say, no pressure," a smiling Drogba added before an ovation from supporters.
The two-time African Footballer of the Year said he had decided to join Montreal after being impressed by Saputo. "The president's speech persuaded me. It was very simple, very warm," he said.
Drogba, meanwhile, revealed he had been surprised by the turnout that marked his arrival at the airport on Wednesday. "I didn't expect that," he said, adding that he did not think his new team-mates would treat him like a superstar.
"It's only the way the people look at you - in the dressing room all the players are the same," he said.
Drogba added he had sought a move to the MLS because he wanted to play regularly after a farewell season at Chelsea last year where he was used mostly as a squad player.
"I wanted to be out on the pitch more," Drogba said, explaining his decision sign an 18-month contract, adding that he still "dreamed of winning trophies."