ondogbia, 27, has joined Atletico on a four-year deal for an undisclosed fee.
He is seen as a replacement for Ghana international Thomas Partey, who joined Premier League club Arsenal on transfer deadline day.
Under La Liga rules, Atletico were granted an extra 30 days outside the transfer window to replace Partey, as his release clause had been paid.
“The box-to-box footballer is a strong presence in midfield and contributes defensively and offensively,” is how Atletico’s website describes Kondogobia.
The France-born player previously impressed at Spanish side Sevilla before spells at Monaco in the French top flight and Inter Milan in Serie A.
He played five friendly internationals for France before swapping allegiances to the Central African Republic (CAR) in 2018 and has since played three times for them.
Kondogbia played in three of CAR’s qualifiers for the 2019 Africa Cup of Nations as they failed to progress to the finals in Egypt.