Much was expected of Kondogbia when Inter forked out $A44.6 million to sign him from Monaco in 2015.
He made 26 Serie A appearances in his debut season at San Siro and a further 24 last term, but new coach Luciano Spalletti has been keen to remould his squad after Inter finished seventh last term.
The Nerazzurri have signed Borja Valero and Matias Vecino from Fiorentina during the transfer window, pushing Kondogbia down the pecking order in Inter's midfield.
Valencia have consequently made their move, marking a return to LaLiga for the France international after he represented Sevilla between 2012 and 2013.
He reunited with Jeison Murillo at Mestalla after the Colombia defender joined on a two-year loan from Inter earlier this month.
Valencia won their season opener 1-0 against Las Palmas on Friday.