Rothwell moves to Ibrox, signing a deal to 2028.
He said, "I am delighted to have the deal done and be here. It is brilliant. The size of the club speaks for itself and as soon as the interest was there it was an immediate yes from me.
“With Russell coming in too it made that decision a little bit easier because working with him in the past and I know what type of guy he is and how he wants to do things. That was an even bigger pull for me, but the club speaks for itself.”
New Gers manager Russell Martin also stated: “He is a player who we thoroughly enjoyed working with during my time at Southampton.
"His leadership, professionalism and quality were a huge asset. He is joining on the back of two promotions so helps bring a real winning mentality to the group.
"We are excited for Joe to join up the squad, get to know his teammates, and help make the group stronger.”