The forward has scored 15 league goals this season on-loan with The Seagulls, and joins for good from Bournemouth.
The Seagulls have sealed a deal for the Bournemouth forward which BBC Sport reports to be on a two-and-a-half-year-deal, for an undisclosed fee.
Brighton's Glenn Murray in action with Sheffield Wednesday's Tom Lees
Since making the switch across the south coast, Murray, 33, has scored 15 league goal in his second spell with Brighton, where he netted 56 goals in 118 appearances between 2008 and 2011 - helping Brighton to the League One crown.
The former Rochdale and Crystal Palace man has led his side to a two-point lead at the top of the English second-tier, as Chris Hughton's men look to seal Premier League promotion at the third time of asking, having fallen short in the last few seasons.
With February on the horizon, Seagulls fans have begun dreaming of the promised land and now Brighton have moved for the their star man this term.
Brighton's Glenn Murray scores their second goal
Manager Hughton is delighted to seal a permanent deal for Murray, telling the club's official website: "Glenn has made a big contribution in the first half of the season, not only in terms of his goals, but as a senior member of the squad.
Sheffield Wednesday's Fernando Forestieri looks dejected alongside Brighton & Hove Albion's Glenn Murray
"He has done exactly what we had hoped he would do when we took him on loan from Bournemouth in the summer, and has been a crucial part of our team and squad so far this season. I am delighted that he wants to commit his long-term future to the club."
Brighton travel to the John Smith's Stadium on Thursday to face playoff-chasing Huddersfield Town, with Glenn Murray set to play his first game as a Brighton player for the second time round.
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