The clubs have agreed a £17.4million deal for his move, with Agbadou signing hours before Turkey's 9pm deadline on Friday.
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The deal represents a quick profit for Wolves, which signed Agbadou in January 2025 for just over £16m from French club Reims.
This season, Agbadou added a further 17 appearances, the majority of which came before his departure for Africa Cup of Nations duty with Ivory Coast over December and January.
The defender made his final outing for the club against Bournemouth last Saturday.
At Besiktas, Agbadou has penned a deal to 2030.