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The Scot, 38, was honoured at the SSE Hydro arena in Glasgow.
"It's very hard not to get emotional when you hear amazing words from people you respect and get this amazing reception," said Hoy.
"I never thought I'd see my name alongside Sir Steve Redgrave, David Beckham and Seve Ballesteros."
He added: "I became a dad eight weeks ago. He was in hospital for eight weeks and finally came out last week and we got him home.
"I'm sure he'll be watching it on telly."
Four-time Olympic cycling gold medallist Sir Bradley Wiggins has paid tribute to the 11-time world champion.
"He is the marker for everybody else because he was, in some ways, the model athlete off the bike as well as on it," said Wiggins, the 2012 Sports Personality of the Year after winning the Tour de France.
"He's right up there, not only for British athletes but in terms of world athletes. I put Chris up there with the Usain Bolts of this world."
Hoy was the first British Olympian for 100 years to claim three golds at one Games at Beijing in 2008, having won his first Olympic title in Athens four years earlier and a silver at Sydney 2000.
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The track cyclist from Edinburgh picked up the BBC Sports Personality of the Year award in 2008 following his hat-trick and was given a knighthood in the New Year Honours list.
At the 2012 Olympic Games in London, Hoy claimed his fifth and sixth gold medals - the most won by a British athlete in Olympic history.
He also secured two gold and two bronze medals for Scotland at the Commonwealth Games.
Barbara Slater, BBC Sport director, welcomed the award for Hoy, who has turned his attention to motor racing since his retirement from cycling in 2013.
"As a former BBC Sports Personality of the Year winner, Sir Chris Hoy has been a tremendous ambassador for sport and, although he has retired from cycling, he continues to be an inspiration to young athletes," she said.
"It's fantastic that he is not only being recognised for his exceptional achievements, but also that it is being awarded to him in his home country."
Six-time Olympic cycling gold medallist Sir Chris Hoy was given the lifetime achievement award at the BBC Sports Personality of the Year.