The 30-year-old has signed with the club until the end of 2026, with FC Kosice holding an option to extend his contract into 2027.
Wollacott has been without a club since leaving English side Crawley Town in July after spending the 2025/26 season with the League Two club.
The goalkeeper made 25 appearances for Crawley last season, keeping six clean sheets as they finished 14th in League Two.
Wollacott will now continue his career in Slovakia as he looks to regain regular playing time and push for a return to the Ghana national team.
The former Swindon Town goalkeeper has earned 11 caps for the Black Stars and was part of Ghana's squad at the 2022 FIFA World Cup in Qatar.
He previously played for clubs including Forest Green Rovers, Bristol City, Swindon and Charlton Athletic before moving abroad to join Hapoel Haifa in Israel in 2023.
FC Kosice will hope Wollacott's experience can strengthen their goalkeeping options for the remainder of the 2026 calendar year.
