Barrios, 29, moved to the Ligue 1 outfit on loan having made just four starts in the Russian capital in more than a season there.
The former Borussia Dortmund man said remaining in Europe was a key factor as he found his temporary home in France.
"I wanted to stay in Europe and be at a well-run club and Montpellier offered me this opportunity," Barrios said.
"I want to thank the president [Laurent Nicollin] and the coach [Rolland Courbis] for having confidence in me and for letting me come here. I'm happy to have this new experience and I hope it will be a success."
Barrios was a prominent influence at Bundesliga club Dortmund, scoring 39 league goals there, before struggling at Guangzhou Evergrande in China and Spartak.
The Argentine-born Paraguay international said he was unlucky not to have an impact in the Russian Premier League.
"I went through a difficult period at Spartak. It was the only place where I didn't play. I started by getting injured and my replacement then played well. Football is like that," Barrios said.
"My goal is to integrate well within the team. I'm going to try to do the things I have to in order to help the team finish high in the table."
