The Welshman was the third British cyclist to win the Tour de France and says he hopes for continued success.
Thomas was the first Welshman to win the Tour de France in July, the first Grand Tour success of his 12-year career.
He came top in a public vote, edging out Formula One champion Lewis Hamilton and England captain Harry Kane.
"It's been an amazing year for British sport," he said after the announcement, "and long may it continue".
The other athletes 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.
He became the third British rider to win the Tour for Team Sky, following in the footsteps of Sir Bradley Wiggins and four-time winner Chris Froome.
He previously won two Olympic and three world team pursuit titles on the track.