The winger was born in Glasgow and has made clear has been a long term dream to star at Ibrox.
Rangers are getting a potential coup in signing the winger as Graeme Murty seeks to strengthen his side.
Murphy left Motherwell in 2013 to sign with Sheffield United, before switching to Brighton.
After two years at the Amex, Murphy is being allowed to move on after falling down the pecking order since the Seagulls were promoted to the Premier League.
Brighton supporters have plenty of admiration for Murphy and he is leaving for Rangers on good terms.
Here is a look at how Brighton fans have reacted to Murphy's move...
Only £1m for Murphy? Sounds cheap to me given we paid about that.— Colin Curryer (@colincurryer) January 4, 2018
Also I’ll be sorry to see him leave if he goes. Hope he fulfils his dreams at his boyhood club though. #bhafc
Murphy wasn't praised enough here, always worked hard. Great signing for Rangers! #bhafc— Leo Simpson (@Leo7Simpson) January 4, 2018
Jamie Murphy would walk into any championship team, surely a move to Scotland is a step down for him #Bhafc— Thomas Parrott (@Parrottt92) January 4, 2018
Jamie Murphy is the sort of player that if it was #FM18, you’d tell him that he has “been a fantastic servant to club, welcome back anytime”. Brilliant player, would like to have seen more of him in the Prem. #BHAFC #RangersFC— Cllr Zeglam (@CllrZeglam) January 4, 2018
Rangers are reportedly paying just over £1 million for Murphy as they seek to make him their first permanent signing since the transfer window opened
Murphy is a Rangers fan and it is important the club build around players who are passionate about the club.
Murphy is just the first step in Rangers' latest rebuilding project.