He had been among the frontrunners for the accolade after leading Great Britain to their first Davis Cup triumph in 79 years.
The event was picketed by protesters unhappy over the inclusion of Tyson Fury on the shortlist of contenders.
Later, the controversial boxer apologised on stage for controversial comments which caused a storm in the build-up.
He finished outside the top three in the public vote.
The controversy aside, it was a night to remember for Northern Ireland sport, with a clutch of local winners. They included legendary jockey Tony McCoy and football boss Michael O'Neill.
The main prize, however, went to Murray. He finished ahead of rugby league player Kevin Sinfield, while heptathlete Jessica Ennis-Hill was third.
Murray was presented with the trophy by New Zealand Rugby World Cup winner Dan Carter and Irish boxing hero Barry McGuigan.
Murray said: "I've dedicated my life to this sport, I work as hard as I can every single day to try and make you proud, and I appreciate all of the support."
Earlier, some of Britain's leading medal hopes at next year's Olympic Games led a star-studded parade down the red carpet.
Although protesters were kept well away, their picket coincided with the arrival of the 7,500 audience.
Up to 30 gay and equal-rights campaigners held banners and chanted slogans in protest at Fury's appearance after he made comments allegedly equating homosexuality with paedophilia and joking about being violent to women. However, there was applause as Fury walked onto the stage to be interviewed by Gary Lineker. But asked about the controversy by Lineker, Fury responded: "I've said a lot of stuff in the past and none of it is with the intention to hurt anybody."
Moneyglass-born rider McCoy was presented with the Lifetime Achievement award.
The 20-time champion jockey retired earlier this year having ridden more than 4,300 jump racing winners. Welcoming McCoy on stage, presenter Clare Balding described him as a "national hero".
McCoy said: "Can I just say what an honour and a privilege it is to receive such a prestigious award, especially here in Belfast.
"Being from Northern Ireland, a place that has produced so many talented and successful sports people, it makes tonight even more special."
Golf star Rory McIlroy had jetted in to present the prize.
He said: "It's absolutely fantastic to bring a great event like this home and show what Belfast and Northern Ireland has to offer," he said.
Michael O'Neill, who led Northern Ireland's football team to their first tournament finals for 30 years, was named coach of the year. He received one of the biggest cheers of the night as he walked up to collect his award.
There was recognition for another Northern Ireland man, Damian Lindsay, who received the Unsung Hero accolade.
He set up football coaching for children in the St James' area of west Belfast to prevent young people in his local area from being dragged into anti-social behaviour. Mr Lindsay was selected from 15 regional winners and was presented with the award by comedian Eddie Izzard.
Other headline winners included Carter, one of the stars of the New Zealand side which won this year's Rugby World Cup.
He was named Overseas Sports Personality of the Year.
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