Kondogbia has signed a contract running until 2022 and the transfer fee is reported to be in the region of €25 million (£22m/$29m).
Valencia have confirmed the 25-year-old's deal contains a release clause of €80m (£70m/$93m).
"I'm very happy and proud to be part of this team," he told the club's website. "Valencia is a wonderful club and I want to be part of its history.
"We all know Valencia is an ambitious club, which for me is important. I also want to take a step forward in my career and things are going well."
However, his form was not good enough to earn a place in Didier Deschamps' France squad for the 2018 World Cup.
"Things in football aren't always fair," he told Valencia's club radio station when discussing the snub.
We've got some good news.... pic.twitter.com/0P1BqbBCO1— Valencia CF English (@valenciacf_en) May 24, 2018
"I'm proud of my team and myself. I've done my job but it's not just that, there are other factors that count in order to get the call-up.
"I knew it would be difficult but the most important thing is that we have done a great job and we are happy.
"The work is done and the performance of each player has improved."