The 26-year-old Scot, who was not at the awards ceremony in Leeds because he is training in Florida following a back injury, edged out Wales and British & Irish Lions rugby union fullback Leigh Halfpenny and jockey A.P. McCoy to win the award.
Murray was presented with the trophy by nine-times Wimbledon champion Martina Navratilova.
"Thanks to Martina Navratilova for giving this to me," Murray said. "She's possibly the greatest tennis player of all time.
"I've got a few people to thank - my family first. A lot are there in the crowd. They've supported me since I was a kid, making a lot of sacrifices for me. I couldn't have done it without you."
Murray beat Serbian Novak Djokovic in straight sets in the Wimbledon final in July to become the first home winner of the men's singles at the grasscourt grand slam tournament since Fred Perry in 1936.
The British & Irish Lions rugby union side were named team of the year following their victory in Australia, the Lions' first series win since 1997.
Formula One world champion Sebastian Vettel of Germany claimed the overseas personality of the year prize.
(Reporting by Ed Osmond; Editing by Rex Gowar)
