Nigerian forward Osimhen sealed a move to Napoli on Saturday (AEST), in a deal that reportedly could eventually net Lille €54 million ($82.1 million).
Replacing the 21-year-old will be no easy task, but Yilmaz comes in as an experienced player who can fill the void.
The 35-year-old Yilmaz joins from Besiktas on a two-year contract, with Lille chief executive Marc Ingla describing him as "a true legend in Turkey" and "a real number nine".
"He has the perfect profile to strengthen our squad, integrate into our model of play and bring to the team all his experience," Ingla said.
Yilmaz said in a news conference: "I want to write a new chapter in my career with Lille."