Murray polled 247,419 votes – more than twice that of his nearest challenger, triathlete Alistair Brownlee. Veteran showjumper Nick Skelton was a close third.
The award capped a vintage year for Murray, who won his second Wimbledon title, defended his Olympic gold medal at the Rio Games and secured the coveted year-end No1 ranking by winning the ATP World Tour Finals.
“It has been a great year for British sport and I am so proud to have been a part of it,” said the Scot, speaking from his winter training camp in Miami.
“I’d also like to thank my family. I think my mum is in the crowd there [at the awards show]. I’d like to thank my dad as as well, who just got married 10 days ago. I miss you guys.
“A huge thanks to my wife and my daughter. She won’t know what this means yet, but maybe in a few years she will.”
He then quipped: “Actually, I’ve got a bone to pick with my wife because about an hour ago she told me she’d voted for Nick Skelton. Not smart from her with Christmas coming up.”
Murray, who also won the vote in 2013 and 2015, received the trophy from former boxer Lennox Lewis in a tongue-in-cheek nod to their awkward third-place presentation ceremony in 2012.
Brownlee defended his Olympic title in Rio but was also widely praised for helping shattered brother Jonny across the line at a World Series event in Mexico later in the year.
Skelton won showjumping gold at the Olympics aged 58 – 16 years after suffering a double neck fracture that he thought had ended his career.
He polled 109,197 votes – twice as many as double Olympic champion Mo Farah in fourth.
Paralympic showjumping champion Sophie Christiansen was fifth, with victorious Team GB hockey captain Kate Richardson-Walsh sixth.