The 33-year-old scored six goals in 12 appearances last season after signing for the club in January.
He helped the club finish as runners-up in the Turkish League last season.
"I'm very excited to announce that we'll be extending our journey together. Special thanks to everyone that is part of the Istanbul Basaksehir," he posted on social media.
The Togo captain moved to Turkey following the Africa Cup of Nations in Gabon in January after being without a club for six months.