The 24-time Super Lig champions confirmed that they would be paying the Nigeria star a salary of six million euros for the 2024/25 season.
The Italian outfit also stated that they had extended Osimhen's contract until 2027.
"When I heard about Galatasaray's interest, it was an easy decision for me. I knew that Galatasaray was big and felt like a family. (Henry) Onyekuru was already a friend of mine and he had told me about it before," he said.
"(Dries) Mertens is like a big brother to me. I'm happy to be teammates with him again. I'm looking forward to meeting my other friends."
Osimhen arrived in Istanbul in the early hours of Wednesday morning to put the finishing touches on a deal, days after proposed moves to Chelsea and Al Ahli failed to materialise.
With most European transfer windows closing at the end of August, Osimhen had to remain at Napoli but was left out of the squad after his relationship with the club disintegrated over the previous 12 months.
With the Turkish transfer window still open, Galatasaray made an offer to take the player on loan, which ended up being the perfect solution for all parties.
"Victor is a very important transfer. Our expectations are very high, especially in our competition in Europe and Turkey. I am sure he will reciprocate. We are pleased to have such world-class players in our team. I wish him success," Galatasaray President Dursun Ozbek said.
Galatasaray currently sit second in the Super Lig, one point off rivals Fenerbahce but with a game in hand. They will also take part in the Europa League this season.
