Molinari, who won the British Open and became the first player to go 5-0 at the Ryder Cup, won an online vote.
Francesco Molinari was named the BBC World Sport Star of the Year at the BBC Sports Personality awards.
Molinari, 36, enjoyed the best year of his career in 2018. The Italian won the British Open, became the first the player to go 5-0 at a single Ryder Cup and won the European Tour's season-long points race, the Race to Dubai, as well as that tour's Golfer of the Year award. He sits seventh in the Official World Golf Ranking.
"It's unreal, to be honest," Molinari said upon receiving the award.
"I'm super proud to be here tonight. There are so many inspirational sporting stories. It gives us more motivation for next season."
Molinari won an online vote to become the first golfer to win the award since 2000, when Tiger Woods won what was then known as the Overseas Sports Personality of the Year. The three other nominees were American gymnasty Simone Biles, Czech skier/snowboarder Ester Ledecka, and Ukrainian boxer Oleksandr Usyk.