The former Manchester City and Arsenal striker on Monday joined Turkish Superlig side on a two-year deal.
Adebayor joins as a direct replacement for Gyan, who departed the Anatolian Stars this summer after spending two years there.
Gyan moved to Turkey in 2017 but struggled to replicate his best form due to a series of niggling injuries.
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The Black Stars General Captain made just 26 appearances and registered just five goals during his time at Kayserispor.
The Turkish club subsequently decided not to renew his contract following its expiration and signed Adebayor as his replacement.
Like Gyan, Adebayor has also played in Turkey for the past two years, having joined Istanbul Basaksehir in 2017.
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The Togo star is expected to make his debut on Friday when Kayserispor host Galatasaray in their third league game of the season.