In January, the two clubs came to an agreement over a loan deal and the winger has since gone on to score five times in 19 appearances in all competitions.
Murphy's form has resulted in the Scottish giants handing the wideman a three-year contract, and the player has admitted that he is delighted to return north of the border.
The 28-year-old told the club's official website: "I'm delighted to make my move to Rangers permanent. This club means a lot to me and it already feels like home.
"Whilst I'm naturally disappointed we didn't complete the objectives that we set for ourselves last season, I am more determined than ever to help this club to be a success."
The Scot leaves Brighton having scored 10 goals in 83 appearances in all competitions.