He was absent as Napoli, the freshly crowned Serie A champions, resumed training at the start of the week as the finer details of the deal were concluded.
Napoli coach Antonio Conte seemingly did not have the 26-year-old in his plans for his side’s Scudetto defence next term.
Negotiations with Galatasaray had been ongoing for several weeks, but up to Thursday had stalled over the terms of payment for the transfer.
Napoli recently recruited Kevin De Bruyne from Premier League club Manchester City.
Osimhen becomes Galatasaray’s most expensive player ever.