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 show jumping 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.
"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 well, who just got married 10 days ago.
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"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.
American teenage gymnast Simone Biles was named Overseas Sports Personality of the Year for her four gold medals and bronze in Rio.