The 33-year-old former Ibrox star has signed a one-year deal with the Cypriot club, subject to a medical, as they become the 14th club of his nomadic career.
Lafferty left Kilmarnock after their relegation to the Championship earlier this month amid a war of words with the Ayrshire side around the circumstances of his departure.
Despite the bad blood surrounding his departure, Lafferty impressed at Rugby Park as Killie’s stay in the top-flight ended, scoring 13 goals in 13 games for Tommy Wright’s side.
Lafferty had two spells at Rangers as well as stints with Sion, Palermo, Norwich City, Rizespor, Birmingham City, Hearts, Sarpsborg, Sunderland and Reggina in his well-travelled career.
During his time at Ibrox, Lafferty won three Scottish Premiership titles, a Scottish Cup and two Scottish League Cups, all coming during his first stint at the club.
The Northern Irishman is his country’s second-highest goalscorer of all-time with 20 goals to his name in 81 appearances, second to another ex-Rangers star in David Healy.
Famagusta are managed by former Newcastle star Temur Ketsbaia and finished fourth in the Cypriot First Division last season.
Originally based in Famagusta, the club is now based in Larnaca and have played there games there since 1974.