The move is expected to become permanent in the summer transfer window but Murphy leaves the Seagulls with fond memories.
He was part of the squad which went so close to promotion in 2015/16, a year before Murphy and his teammates eventually secured an historic promotion to the Premier League in 2017.
Murphy found first-team opportunities limited this season and has now joined Rangers, the club he supports, on loan. He tweeted last night: "Wore the shirt many times as a kid but the chance to put it on for real is something special. Will always be worn with pride. Thank you all for the support!
"Thank you to everyone at @OfficialBHAFC for the support over the last few years. Winning promotion with the group of boys we had is something I will always remember. All the best!"
Brighton manager Chris Hughton said: “Jamie is a great lad, a fantastic professional and has a desire to play - and while we were in no hurry to see him leave, we do understand his desire to play for his boyhood team and one of the biggest clubs in Scotland.
“He’s been excellent for the club, ever since we signed him from Sheffield United, and wrote himself into club folklore as a crucial part of our promotion-winning side last season.
“On behalf of all at the club, I’d like to thank Jamie for his efforts and achievements during his time here and wish him the very best for the future.”