Madeley described Vine as "a true and utter gentleman at all times."
He added: "I don't know of anybody who is regarded as he was in terms of his professionalism and dedication, whether he was presenting or commentating.
"He was like a member of my family. He was that close."
In 1967, Vine was the first presenter to introduce Wimbledon in colour and hosted the BBC's highlights programme until 1982.
From 1978, the World Snooker Championships received daily coverage on the BBC and Vine again took care of presenting duties until his retirement in 2000.
He also anchored the Grand Prix, UK Championship and the Masters.
Vine's last broadcast for the BBC was as a weightlifting commentator at the 2000 Olympics in Sydney, after which he retired because of a heart condition stating, "I've got to go some time, and now is the right time."
Roger Mosey, director of BBC Sport, paid tribute to Vine "as a wonderfully versatile presenter".
A Question of Sport was just one of the many programmes Vine hosted
He continued: "It is a tribute to his abilities that he was associated with so many events.
"He was the face and voice of Ski Sunday, of course, but also brought among others snooker, show-jumping, A Question Of Sport, Superstars and Olympic sports to millions of viewers. They and we will remember him with great affection."
Minister for Sport Gerry Sutcliffe described Vine as "one of sports broadcasting's great all-rounders, a familiar figure on our TV screens across four decades.
"As the face of the BBC's coverage of the snooker world championships from The Crucible and Ski Sunday, he helped popularise emerging and growing sports.
"But he could turn his hand to almost anything - the first presenter of A Question of Sport, host of Superstars, commentator on It's a Knockout, a regular fixture at Wimbledon and the Olympics - and much more.
"We have lost a great enthusiast for sport and a considerable broadcasting talent."
Individuals from the world of snooker have been quick to praise Vine, who spent a quarter of a century working on the sport's major tournaments.
Dennis Taylor, on whose epic World Championship final win against Steve Davis in 1985 Vine commentated and earned an audience of 18 million, described him as "the face of snooker".
Seven-time World Champion Stephen Hendry echoed these sentiments.
David Vine's snooker memories
"He was the face of snooker for many years," he said.
"In my first experiences of The Crucible he made me feel very welcome and through the years I got friendly with him and had some laughs. It's very sad."
Terry Griffiths, on whose 1979 World Championship win Vine commentated and later became his colleague at the BBC, said: "He had that wonderful voice that gave you the feeling that if you were in fog it would come through.
"He knew the game so well and he knew the players so well, that's what was special about David."
He leaves behind three children from his first marriage, a son from his second marriage and four grandchildren.
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