The Black Eagles are reported to have reached an agreement with the Germany international over a three-year deal.
Gomez is expected to arrive in Istanbul on Thursday before undergoing a medical and being officially unveiled in a signing ceremony.
The 30-year-old striker has become the Istanbul giants fifth transfer of the season following the transfers of Andreas Beck, Dusko Tosic, Ricardo Quaresma and Rhodolfo.
Hurriyet report that the experienced striker will make €4 million – before bonuses – and an additional €1.5 million signing on fee.
Gomez would become the highest paid player in the current Black Eagles side should he receive €5.5 million in his first season at the club.
The Germany international would be replacing Demba Ba who was the Istanbul giants top scorer last season with 27 goals in all competitions for the Black Eagles.
Ba was signed by Chinese giants Shanghai Shenhua for a €14 million fee last season.