Tunisia's Skhiri heads to Bundesliga new boys Cologne
"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.
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.