The 25-year-old, who has recently been linked with Tottenham Hotspur, spent the 2017-18 campaign on loan at Valencia - scoring four times in 36 appearances for Los Che.
The former Spanish champions have now completed the permanent transfer of the midfielder, who has signed a contract until the end of the 2021-22 campaign.
"I'm very happy and proud to be part of this team," Kondogbia told the club's official 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."
Valencia, who finished fourth in La Liga last term, have confirmed that Kondogbia's release clause will stand in the region of £70m.