The 31-year-old Peruvian international was released by the Viola this summer at the expiry of his contract after seven seasons with the club, which included a loan spell at Genoa sandwiched in between.
After an impressive start to his Fiorentina career, Vargas began to slowly drop down the pecking order in Florence, and was more of a fringe player in his final years with the Serie A side.
According to Firenzeviola.it, Vargas is ready for a new adventure in Spain, and has reached an agreement with the newly promoted La Liga outfit for a two-year contract.
It is believed that former Fiorentina director Eduardo Macia, now at Betis, was crucial in bringing Vargas to the Andalusian club given his knowledge of the left-sided player.
Vargas made 186 appearances for the Viola during his stay at the club, netting 25 goals.