The transfer fee remains undisclosed, and Roerslev has signed a four-year contract that will keep him at St Mary's until 2029.
Saints' technical director Johannes Spors praised Roerslev, saying, "He comes to us with a lot of experience from the Premier League and the Championship. He knows what it takes to succeed in the top division."
Spors also noted that Roerslev is joining the team at a good age, at 26, and will be able to contribute to the team in the short and long term.
Roerslev expressed his excitement about joining Southampton, saying, "I'm happy to be here and can't wait to get started. I had great talks with the coach, and I feel that Southampton is a team that suits my playing style."