The 21-year-old, who scored 13 and assisted five goals in Ligue 1 this term, only joined Lille from Belgian side Charleroi following Pepe's move to north London a year ago.
But Osimhen's performances in his debut campaign were enough to see him named in the French top flight's team of the season, and have now earned him a big money move to Serie A.
Having started his professional career with Bundesliga outfit Wolfsburg, for whom he failed to score a single league goal, the Nigerian will have played in three of Europe's five major leagues before his 22nd birthday.
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