Roerslev moves to St Mary's for an undisclosed fee, penning a four-year contract to 2029.
Saints technical director Johannes Spors said: “Mads comes to us with lots of experience, both in the Premier League and in the Championship. He knows what it takes, not only to win promotion from this division, but to build on those foundations at the very highest level.
“At 26 years old, he arrives at a good age to help us in the short term, as well as in the seasons ahead.”
Roerslev said: “I’m a happy guy, very excited to get started. I had some very, very good talks with the coach and I’m coming here to play.
“I see Southampton as a really good team who controls a lot of games, works hard and suits my way of playing. It was just an overall positive feeling about everything.”