The Northern Ireland international was one of a number of players who departed the Scottish outfit when the club fell into administration last year.
"On the day it was announced Rangers were going into administration it was just a series of words to us until we absorbed the ramifications of what had taken place," Davis told reporters.
"I had just signed a new, five-year contract and it had always been my intention to honour that agreement and devote the largest part of my career to the team I considered to be one of the biggest names in world football.
"I loved the club and the fans but I had to take a decision which was best for me, my family and the remainder of my career. There was so much uncertainty, so I was delighted Southampton made an acceptable offer.
"If everything goes to the plan I have in my head I'd like to come back and play for the club again before my career ends. I still follow Rangers and they continue to mean a lot to me."
Davis scored in Southampton's 3-1 win over Manchester City last weekend.