Raducanu, who is isolating in Abu Dhabi after testing positive for Covid-19 on arrival in the United Arab Emirates last week, told the BBC: “It’s such an honour just to be among these nominees – to win it is pretty amazing.
“I watched Sports Personality of the Year growing up, so I’m really humbled to join the amazing past winners – I’m also really happy for British tennis that we managed to get this award again.
“All the support I’ve received this past year has been absolutely insane, and the energy I felt at Wimbledon this year playing in front of my home crowd is something I’ve never felt before.”
Raducanu entered the New York tournament ranked 150th in the world and now has to contend with additional pressure on her shoulders, but she insists her family have helped to keep her grounded.
Speaking before her victory had been announced, Raducanu said: “The self-belief, I feel like I just had that as a child growing up.
“It’s been instilled into me from a young age and I think sport gave me that inner belief and confidence.
“I feel completely the same and everyone around me is definitely the same and keeping me in my place.
“My parents are never ones to really make a big deal out of anything that I do that’s good, so we’ll see. They have been normal, nothing too big, nothing too low, that’s just the way they have brought me up.”
Diving star Daley, who had missed out on gold at three previous Olympic Games, finally took the top step on the podium in Tokyo alongside his 10m synchro partner Matty Lee.
Speaking before the award top three was announced, he said: “Honestly (winning gold) was a dream come true and something I never thought was ever going to happen to me.
“I knew that I could do it I but I was almost ready to settle for the fact that I was never going to do it.
“I was a blubbering mess. I had this whole dream of standing on the podium, the national anthem would play and I’d be able to sing at the top of my lungs and I literally couldn’t even breathe.”
Tyson Fury, Raheem Sterling and Dame Sarah Storey were the other three individuals shortlisted for the award, with Sir Lewis Hamilton, who came so close to winning a record eighth Formula One title earlier this month, omitted.
Gareth Southgate won the Coach of the Year award after steering the England men’s football team to their first major final in 55 years at Euro 2020 in the summer.
They were beaten on penalties by Italy in the final at Wembley, but their achievement was recognised with the Team of the Year accolade.
Southgate thanked the backroom team around him and told BBC Sport: “Managing in football now is a very complex business.
“I’m fortunate to work with good people that make it easier for me.”
Irish jockey Rachael Blackmore was voted World Sports Star of the Year.
She was the first female jockey to win the Champion Hurdle at Cheltenham in March and followed that up a month later with victory at the Grand National – the first woman to triumph in the race.
Skateboarder Sky Brown, 13, won the Young Sports Personality of the Year. She became Britain’s youngest-ever Olympic medallist when she took bronze in the women’s park event.