The Welshman, whose victory in cycling's most prestigious race was the sixth by a British rider in seven years, topped the public vote ahead of Formula One world champion Lewis Hamilton and England soccer captain Harry Kane.
Thomas was the first Welshman to win the award, presented by Tennis legend Billie Jean King, since soccer player Ryan Giggs in 2009.
"I feel very lucky to have come into cycling when I did. I just went down to the local leisure centre for a swim and instead I rode my bike," Thomas said.
Although he had previously been a double Olympic champion on the track, he had lived in the shadow of four-times Tour de France winner Chris Froome in Team Sky until beating his team-mate and defending champion in the 2018 race.
"As a bike rider, I always focus on myself. Obviously, people want me to win, but hearing stories like Tyson (Fury)'s and Billy (Monger)'s, you realise that what we do does inspire people back home," Thomas said.
Fury amazingly beat the count after being knocked down in his world heavyweight title draw with Deontay Wilder while youngster Monger made an uplifting comeback to motor racing after having his legs amputated following a Formula 4 crash.
Geraint Thomas speaks after winning the BBC Sports Personality of the Year award during the BBC Sports Personality of the Year 2018 at Birmingham Genting Arena. Source: AAP
The others short-listed for the award were triple European sprint champion Dina Asher-Smith, English cricket's record test wicket-taker James Anderson and double Olympic skeleton champion, Lizzy Yarnold.
It completed a happy day for the 32-year-old Thomas at the end of an unsettling week in which Sky, sponsors of Team Sky, announced it would end its involvement with his team at the end of 2019.
Thomas picked up a replica of the winner's trophy from Tour de France organisers earlier on Sunday after the original was stolen from a cycling show.
Gareth Southgate, who led England's soccer men to the World Cup semi-finals, won coach of the year while the England women's netballers who took Commonwealth Games gold won team of the year.
Italian golfer Francesco Molinari, star of Europe's Ryder Cup win and British Open champion, was voted World Sport Star of the Year.
