The distance runner, who won his sixth world championships gold medal in London this year when he triumphed in the 10,000 metres, was named the winner ahead of second-placed superbike rider Jonathan Rea and para athlete Jonnie Peacock.
Pre-event favourites, world heavyweight boxing champion Anthony Joshua and Formula One world title holder Lewis Hamilton, failed to make the top three.
Farah, who was born in Somalia and moved to Britain at the age of eight, won 5,000m and 10,000m gold at the 2012 and 2016 Olympics as well as six world titles in those distances.
The 34-year-old, who ended his track career this year to concentrate on road running, looked stunned when he was awarded the trophy by his step-daughter Rihanna in a studio in London.
He was denied the chance to tell viewers how he felt as the BBC's live satellite link to the ceremony in Liverpool's Echo Arena cut out seconds later.
After the show went off air, Farah, appearing close to tears, spoke to those inside the arena saying he was shocked to win due to the quality of the other athletes.
“It is pretty amazing and hard to think about. I didn’t imagine I was every going to win this but... anything can happen. If you work hard you can achieve your dreams.
Other winners included:
Overseas Sports Personality of the Year - Swiss Roger Federer for winning a record eighth Wimbledon tennis title and taking his overall grand slam tally to a record 19
Lifetime Achievement - retired Olympic heptathlete champion Jessica Ennis-Hill
Coach of the Year - Benke Blomkvist, Stephen Maguire and Christian Malcolm for guiding Britain's men's 4x100m team to world gold
Team of the Year - England women's cricket team for winning the World Cup by beating India in the final
(Reporting by Pritha Sarkar, Editing by Ken Ferris)
