The French defender leaves Liverpool after six years, having joined in 2018 from Orleans.
Koumetio has joined Dundee on a two-year contract.
He told the club's website: "It feels very good to join the club, I am really happy to be here. I believe and have the conviction that this is the best step in my career.
"I had discussions with the manager, Liverpool and my agent and once we reached an agreement everything went through. I discussed with the manager how he wants to play and how he wants me to play and how I can improve as a player. I spoke with Owen Beck about his time at Dundee and he loved it, everything he said about the club was so positive.
"All the Liverpool lads all saw how Dundee helped develop Owen. I can’t wait to play in front of the Dundee fans, I love the support that the supporters give, they help us so much to play.”