Remy, 23, was diagnosed with a heart defect last week after joining on a five-year contract from Nice.
The striker, who has two international caps, underwent further tests on Monday and results showed he could safely play at the highest level.
"A panel of medical experts said the results were reassuring," Olympique Marseille doctor Christophe Baudot told reporters.
The player had feared he might never play football again.
"You're not in the best conditions when you're told your career could be over," he said. "But now I feel relieved. It's taken a weight off my mind and I'm ready to play on Sunday."
Marseille coach Didier Deschamps said Remy would be included in the squad to face Bordeaux in Ligue 1 next weekend.
Marseille president Jean-Claude Dassier said he would ask Nice why they did not inform them of Remy's problem before they sold him.
The incident was reminiscent of June 2008 when former France defender Lilian Thuram was unable to sign for Paris St Germain and had to end his career after having a heart condition diagnosed during a medical.
Last year, forward Steve Savidan's move from Caen to Monaco collapsed for the same reason and he too had to hang up his boots.
Remy started out at Olympique Lyon and joined Racing Lens in 2007 before moving to Nice the following year. He scored 14 league goals last season.
Marseille bagged their first points of the season with a 2-0 home win against Lorient last Saturday. They had lost their first two games.
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