The Italian champions have offloaded the attacking midfielder to the Romanian club, where he will have the chance to feature in the Champions League
The Uruguayan midfielder was no longer needed by the Serie A giants, and will now try and re-launch his career with the Transylvanian Champions League hopefuls.
Martinez joined Juventus from Catania in the summer of 2010, but never really managed to secure regular first team action at the Turin side.
The 29-year-old had been farmed out on loan to Cesena last season, and will spent the 2012-13 campaign at Cluj, who are the reigning champions of the Romanian league.
Martinez has a contract with Juventus until the summer of 2014.