The 58-year-old former German international striker scored nine goals playing for Istanbul-based side Besiktas in 1995-96.
Kuntz, who has established his coaching reputation on the back of coaching Germany to two European Under-21 titles (2017/21), looked back on those days with longing while formally signing his contract to replace Senol Gunes as Turkey's new head coach.
"Its like coming home. It was an unbelievable one year in Besiktas," Kuntz told reporters at the signing ceremony in Istanbul.
"My wife even still tells me we made a mistake, that we left Turkey too early."
No financial terms of the deal were disclosed.
The football federation decided to part ways with Gunes after Turkey got thumped by the Netherlands 6-1 in a 2022 World Cup qualifier earlier this month -- one of the worst losses in their history.
Turkey are sitting third behind the Netherlands and Norway in World Cup qualifying.