The 27-year-old, who wore his country's colours in all four of Ghana's World Cup matches this summer, has signed a contract running until 30 June 2028 and will wear the number 14 shirt in Cologne.
Although Koln also have Luka Lochoshvili, capable of covering the left side of defence, the club had searched for a specialist left-back for some time before turning to Mensah, whose contract at Auxerre had run down.
Sporting director Thomas Kessler explained the move: "We've been looking at Gideon for some time now and we're delighted we were able to bring him to the club. He brings international experience, showed strong performances in France last season and confirmed that form at the World Cup.
"Gideon is a player who consistently puts himself at the service of the team and impresses on the pitch with high tactical discipline, defensive strength and dynamism.
"With his profile he will give our squad extra quality and stability and further improve our options in that position."
Mensah also expressed his excitement at the move: "From my conversations with the people at the club, who worked hard to bring me here, I had the best feeling right from the start. On top of that there's the sporting perspective the club showed me.
"And of course I've already heard a lot about the city and the exceptional support of the FC fans, which I'm really looking forward to. Just as I did for Ghana and my previous clubs, I'll give everything for FC too, so the club can reach its goals and we can be successful as a team."
Mensah's performances in Ghana's run to the World Cup group stage also attracted interest from Schalke, though Cologne moved decisively to complete the signing. The club have indicated Mensah will not be the only addition to the left side of defence this summer, with a further left-back still being sought to provide competition for the Ghanaian.
A product of the West African Football Academy, Mensah began his European career at Red Bull Salzburg before loan spells at Sturm Graz, Zulte Waregem, Vitoria Guimaraes and Bordeaux, eventually joining Auxerre permanently in 2022. He went on to make 114 competitive appearances for the French club, 85 in Ligue 1, and has earned 44 caps for Ghana since his international debut in 2019.