The 26-year-old, who ended Britain's 77-year wait for a men's singles champion at Wimbledon this year, was presented with the famous trophy by former tennis star Martina Navratilova after topping the public vote.
The Scot, who was overwhelming favourite to win the prize, beat British and Irish Lions rugby union player Leigh Halfpenny who finished second and horse-racing jockey AP McCoy in third place.
Sir Alex Ferguson was presented with a special Diamond award, for the progamme's 60th year, to mark his achievements as Manchester United and Aberdeen manager.
Murray did not attend the ceremony as he undergoes rehabilitation in America following back surgery.
Appearing via a satellite link from Miami, Murray thanked the public for their support over the last two years which he said had made "a huge difference" at Wimbledon.
"I couldn't have done it without you," he said.
"I know sometimes I'm not the easiest person to support but I've had a lot of pressure on me for a long time so I'm just glad I managed to break through."
Murray joked that "no matter how excited I try to sound my voice still sounds incredibly boring".
"I'm very happy and excited right now," he said. "That's just my voice, I'm sorry."
A visibly emotional Murray apologised for not attending the star-studded event, which took place in front of an audience of thousands at the First Direct Arena in Leeds and millions of viewers watching on television at home.
"I couldn't have got to the position I'm in if I didn't take my training and my preparation extremely hard," Murray said.
"I've dedicated probably the last 10-15 years of my life to this so thank you very much everyone and I'm sorry I couldn't be there."