The Chile international will spend the 2013 season in the Brazilian top flight after a difficult one-year spell with the Partenopei during which he failed to secure a regular berth
The versatile attacker joined the Partenopei from Universidad de Chile in January 2012, but had since failed to secure regular first-team action at the San Paolo.
Therefore, 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 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," sporting director Rui Costa commented on the move.
The Chile international netted only three goals in 15 appearances during his time at Napoli. The Partenopei have the right to recall the player in the summer if they see fit.