The Scottish Premiership side will have the exclusive option to sign the 28-year-old on a long-term deal in the summer for a guaranteed fixed fee.
Murphy made 35 league appearances as Brighton earned promotion from the Championship last season but has made only four Premier League appearances this season, three as a substitute.
"Jamie's a fantastic professional, a great lad, and has a desire to play," Brighton boss Chris Hughton told reporters on Saturday.
"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."
Murphy played for Motherwell before moving to Sheffield United in 2013, spending two years at Bramall Lane and subsequently joining the Seagulls in 2015.