The Northern Irishman is a free agent after departing Kilmarnock following the team’s relegation to the Championship.
Famagusta have confirmed the striker has agreed a one-year deal and it will be confirmed once he “completes the necessary medical examinations”.
Lafferty scored 13 goals in 13 games for Killie last season having joined after exiting Serie B side Reggina 1914.
His goals were unable to keep Killie up and his departure turned somewhat sour.
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The club released a statement wishing to clarify remarks made by the 33-year-old in the media.
Lafferty claimed he was given only a few hours to decide on a new contract, something Kilmarnock said was “simply not true”.
Famagusta, who finished fourth last season, will be the player’s 14th club in a career which has taken him to Italy, Norway, Switzerland, Turkey and now Cyprus.