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"The move to the Bundesliga comes at the right time for me," the 24-year-old told the German club's website.
"Cologne have taken a real interest in me and fully convinced me of the move. (They) are a big and exciting club with plenty of tradition, which I can identify with really well."
Skhiri, who has signed a four-year deal, had been with Montpellier as a youngster since 2010 and played 133 games since his senior debut in 2015 before being named vice-captain.
No transfer fee has been released.
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He made the first of his 23 international appearances in March 2018 before featuring three times at the World Cup later in the year.
Montpellier, who finished sixth in Ligue 1 last year, have already signed Teji Savanier and Jordan Ferri as cover for Skhiri ahead of the new domestic campaign which starts against Rennes on August 10.