The Chilean is keen to recover his best form at Gremio, having lost confidence in his ability during his spell at Napoli
The Italian club paid €13.7 million for the 23-year-old's services in January 2012 after Vargas had impressed for Universidad de Chile.
However Vargas only managed 19 appearances for Napoli, and scored all of his three goals in one Europa League match against AIK.
Speaking to reporters, Vargas said he never recovered his confidence after a disappointing debut for Napoli.
“I was not happy in Italy. I didn't feel good on my debut and played badly, then I lost my confidence and was never able to play consistently," he explained.
Vargas also said that Gremio were recommended to him by team-mate Bruno Uvini, and that he hoped he would be able to reproduce the form he demonstrated in Chile for his new side.
“It was my Napoli team-mate Bruno Uvini who recommended Gremio to me.
"He told me all about this city, how relaxed it was and how playing for Gremio would be good for me.
“I had a good career in Chile, now I want to repeat that in Brazil and become one of the best players in the Copa Libertadores.”