The Belgian agreed to sign a one-year contract with the option of an additional year should the Turkish side secure Champions League qualification and would receive €4 million a year.
He is expected to travel to Istanbul to undergo his medical examination.
Mertens became a free agent after spending nine years with Napoli. They had an option to extend his contract until 2023 but decided against activating the clause.
They instead wanted to negotiate a contract extension, but those talks did not materialise as the club did not want to match his salary demands.
Mertens may be past his peak with retirement looming, but that has not stopped several top clubs, including Newcastle United and Marseille, from registering an interest in the striker.
However, Galatasaray have jumped ahead of a long list of potential suitors vying for his signature after enticing him with a more lucrative salary package.
Mertens joined Napoli in 2013 and went on to become the club’s all-time highest goal scorer, recording 148 goals and 90 assists in 397 appearances for the Gli Azzurri. Last season, he scored 11 times in 30 league appearances.
The Belgium international has called time on a fruitful spell at the Diego Armando Maradona Stadium and has already said his goodbyes to the Napoli fans with a move to Galatasaray imminent.
The Turks are also working to sign Lucas Torreira, who, despite impressing while on loan at Fiorentina, is considered a fringe player and is not in Mikel Arteta’s plans.
The Uruguayan may join Okan Buruk’s side in a deal worth around €6.5m.
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