The Nigeria international spent last season on loan with Galatasaray, helping the team win the Super Lig and Turkish Cup Double.
The two clubs had previously agreed on a transfer fee of €75 million, to be paid in two installments: €45 million upfront and €30 million next year.
Napoli's president, Aurelio De Laurentiis, also included a clause that prevents Osimhen from being sold to an Italian club for the next two seasons.
Personal terms with Osimhen were settled several weeks ago, and the only remaining step is for the two clubs to exchange contracts.
