The versatile attacker joined the Partenopei from Universidad de Chile in January 2012, but he had since failed to secure regular first-team action at the San Paolo. Vargas was keen to leave the club on a temporary basis in order to get regular first-team action elsewhere.
The player had initially appeared to be on his way to Sao Paulo, but the 23-year-old has now joined Brazilian foe Gremio instead.
"The negotiations went on for a long time, but I am convinced that it was worth it as Vargas brings quality to the team," Gremio sporting director Rui Costa said.
Vargas netted only three goals in 15 appearances during his time at Napoli. The Partenopei have the right to recall Vargas in the summer if they see fit.