A visibly emotional Hamilton received the most public votes to take the prize weeks after winning his second Formula One world title following a thrilling battle with Mercedes team-mate Nico Rosberg.
He saw off golfer Rory McIlroy, who was the favourite after picking up two majors at the Open and the US PGA Championship, as well as helping Europe to victory in the 2014 Ryder Cup at Gleneagles.
European 10,000m athletics champion Jo Pavey, 41, came third after becoming the oldest gold medallist in European Championships’ history when she won in Zurich in August.
Accepting his award, Hamilton praised his “amazing team” and his family, after admitting he had not expected to claim the honour ahead of McIlroy.
Paul McGinley claimed the Coach of the Year award after inspiring Europe to a five-point victory over the United States at the Ryder Cup in Gleneagles.
Cyclist Sir Chris Hoy, who in 2012 became Scotland’s most succesful Olympian, was given the Lifetime Achievement award.
Host Gary Lineker battled ‘man flu’ to get through presenting duties and the Match of the Day host’s familiar and smooth voice was reduced to at times to a dry rasp.