Murray is in his second spell at the Seagulls but was tipped to exit the Amex Stadium during the winter transfer window after being starved of first team opportunities this season.
Murray’s start against the Hammers on Saturday was just his fourth of the season as his 79th minute equaliser secured a 3-3 draw.
The 36-year-old’s current contract was set to expire at the end of the season, when he would have been a free agent.
Murray has scored 111 goals in 278 games for Brighton in all competitions and needs just 14 goals to overtake Tommy Cook as the club’s all-time leading goalscorer.
Brighton boss Graham Potter said: 'I'm delighted Glenn's agreed this new contract, and it's one he deserves. He's got it because of what he can bring to the team and squad.
'Everyone knows what Glenn brings to the club, and he's an important member of the squad - on and off the pitch - and he showed that in abundance on Saturday at West Ham.
'I've always said he's got a big part to play here. He's happy and settled, he loves this club, and he's been the ultimate professional on and off the pitch. He's keeps himself in fantastic shape and that takes great dedication.'
Brighton are 15th in the Premier League on 26 points, just two points above the relegation zone.
