The 21-year-old attacker spent just a single season in France but showed enough to seal a big move to Serie A, with Napoli understood to have given him a five-year contract.
Nigeria international Osimhen moved to Europe in 2017 when he signed for Bundesliga side Wolfsburg, but he was allowed to join Belgian club Charleroi on loan and it triggered a purchase option on him just last year after scoring 20 times in 2018-2019.
Charleroi quickly made a significant profit on their apparent €3.5 million ($5.8 million) outlay as Lille came calling, bringing him to France in a deal said to be worth up to €15 million ($24.5 million).
During his solitary season in Ligue 1, Osimhen scored 13 goals, a figure bettered by only Wissam Ben Yedder, Kylian Mbappe and Moussa Dembele, and he set up four more in 27 league appearances.
The deal could eventually reach €54 million ($88.7 million), according to claims in Italy, making him Napoli's record signing.
Its previous record signing, Hirving Lozano, has been linked with a move away after an underwhelming first season in Serie A after costing €42 million $69 million) from PSV.