The 29-year-old Murray capped a memorable year in which he claimed his second Wimbledon and Olympic titles, deposed Novak Djokovic as world number one and became a father for the first time.
He beat two-time Olympic triathlon champion Alistair Brownlee and Olympic showjumping gold medallist Nick Skelton in the public vote with the results announced at a ceremony in Birmingham.
"Actually, I've got a bone to pick with my wife (Kim) because about an hour ago she told me she'd voted for Nick Skelton. Not smart from her with Christmas coming up," said Murray who was presented with his trophy at his Miami training base by former world heavyweight boxing champion Lennox Lewis.
Murray, who also won the award in 2013 and 2015, added: "I'd like to thank everyone who voted -- I really appreciate your support.
"Also I'd like to thank my family. I think my mum is in the crowd there (in Birmingham). I'd like to thank my dad as as well, who just got married 10 days ago.
"A huge thanks to my wife and my daughter (Sophia) -- she won't know what this means yet, but maybe in a few years she will."
Leicester City manager Claudio Ranieri was named coach of the year after guiding the Foxes to the Premier League title. Leicester, 5,000-1 to lift the trophy at the start of last season, were also voted team of the year.
Michael Phelps received the lifetime achievement award after winning five Olympic golds in Rio, taking his total to 23 gold and 28 medals in total.
American teenage gymnast Simone Biles was named Overseas Sports Personality of the Year for her four gold medals and bronze in Rio.