After spells with Deportivo La Coruna and Bursaspor, the 24-year-old has penned an 18- month deal with the La Liga strugglers
The 24-year-old joins on a free transfer and has penned an 18-month contract which will keep him at the club until 2017.
Cuenca first made his name under Pep Guardiola in Barca’s first team, but his career in Catalonia was drastically halted due to a succession of injuries.
IN FULL: | January’s done deals
After a loan spell at Ajax and more fitness problems, he left Camp Nou on a permanent basis to sign for Deportivo La Coruna in 2014.
However, despite regularly featuring in La Liga for Depor, he left for Turkish side Bursaspor last summer.
He now joins a Granada side who are fighting against relegation in Spain’s top flight.
Following a 1-0 defeat to Villarreal at the weekend, they find themselves in 19th position in the table, with only Levante below them.