The club have agreed a deal with Valencia which will see them pay €17 million plus variables for the midfielder, who will undergo a medical on Sunday.
Coach Diego Simeone had wanted to add a dominant, box-to-box player in midfield to compensate for the loss of the Ghana international.
Under La Liga rules, Atletico were granted an extra 30 days outside the transfer window to sign a replacement for Partey, as his release clause had been paid.
Kondogbia, 27, had been promised that he would be allowed to leave Valencia by club president Anil Murthy, after a number of their best players — including Dani Parejo, Rodrigo and Ferran Torres — departed Mestalla this summer.
Earlier this month, the French midfielder accused the club of failing to honour their word, posting a message on Instagram which read: “After having destroyed an ambitious project, you had to mislead your coach and, finally, me. Thank you Anil Murthy.”