Sir Henry presented the 1971 award to Princess Anne
Former winners relive the moment they were named BBC Sports Personality of the Year.
Q. What do you remember about the night you won?
A. I had been going to the Sports Review of the Year, as it was called then, since the early 1950s after I turned professional so I had begun to think that maybe I was never going to win it.
I had also been British heavyweight champion for a few years before I actually won it, so you can imagine how delighted I was when I eventually picked up the award.
And as if that wasn't enough, I won it again three years later!
Q. How high does winning Sports Personality of the Year rate when you look back over your career?
A. I rate the Sports Personality award very highly because it is voted for by the public and in those days, there weren't so many television channels to choose from so you knew that most people were watching the BBC.
DID YOU KNOW?
Cooper was the first person to win the award twice - only Damon Hill and Nigel Mansell have done since
I think there must have been about eight or nine million people watching. It was lovely and it is a marvellous compliment to be paid.
I had a great career, over 17 years, and the Sports Review of the Year was a really important part of that.
In fact, I signed my first professional contract with Jim Wicks live on the BBC in 1954.
Q. How did you celebrate afterwards?
A. We always stayed in the studio where they had a party afterwards. Everyone used to stay on and it was always good fun.
I used to enjoy meeting people from other sports and it was a real honour to be among all those famous names.
Q. Who do you consider the all-time Sports Personality?
A. That's a tough one. Even though he never actually won it, I think Roger Bannister would get my vote for breaking the four-minute mile.
But from past winners, I would pick Sir Steve Redgrave for his five Olympic gold medals. He is an incredible athlete.
Sir Henry Cooper was talking to BBC Sport's Caroline Cheese