The 19-year-old became the first qualifier to ever win the US Open in September after triumphing at Flushing Meadows.
Raducanu beat off competition from diver Daley, who was second, and swimmer Peaty in third place, plus boxer Fury, footballer Sterling and Para-cyclist Storey to win the award.
"It’s such an honour just to be amongst these nominees. To win is pretty amazing," said Raducanu, who also reached the fourth round at Wimbledon this year on her Grand Slam debut.
"The energy this year playing at Wimbledon in front of my home crowd - that was something I’ve never felt before."
"I’ve watched Sports Personality of the Year growing up and it’s an honour to be amongst those past winners.
🌟 The first qualifier in the Open era to win a Grand Slam
🌟 The youngest women's Grand Slam champion since 2004
🌟The youngest Briton to win a Grand Slam title
And now...BBC Sports Personality of the Year 2021.
— BBC Sport (@BBCSport) December 19, 2021
"I’m happy for British tennis as well and that we’ve managed to get this award... again."
Britain’s Andy Murray was the last tennis player to win the award in 2016 after claiming the trophy in 2015 and 2013.
Skateboarder Sky Brown took home the Young Sports Personality of the Year award after the 13-year-old won the Olympic bronze for Britain in the women’s park skateboarding final at the 2020 Tokyo Games.
Additional reporting from Reuters