The Ligue 1 club confirmed the move on Tuesday, and have the right to buy the 29-year-old forward at the end of the campaign.
Barrios forged a reputation as a prolific striker during previous spells in Chile and Germany, but failed to recapture that form with the likes of Guangzhou Evergrande and Spartak.
After 37 goals in two seasons with Colo Colo in Chile, Barrios earned himself a move to Bundesliga outfit Borussia Dortmund.
Barrios netted 39 league goals in three seasons at Signal Iduna Park, including 16 in 2010-11 - a tally that helped Dortmund to the first of their back-to-back Bundesliga crowns.
Moves to China and Russia followed for the Paraguay international, with Barrios now arriving at Montpellier hoping to help revive the fortunes of a club which won the Ligue 1 title in 2012, but finished only two points clear of the drop zone last season.