Friends and co-stars all paid tribute to the former dancer, who became head judge on Strictly Come Dancing and its US counterpart Dancing With The Stars.
Strictly presenter Claudia Winkleman called Goodman "a class act" who was full of "twinkle, warmth and wit".
Respects were also paid by the British Royal family and UK government.
Former Strictly judge Dame Darcey Bussell said: "He had the gift of the gab, and I will never forget his use of fruit and veg and sticky toffee pudding as descriptive phrases of dance.
"He was always professional: grounded, funny, loveable, supportive and respectful… but never shy to say how it was.
"For Len, Strictly and Dancing with the Stars was never about the fame, it was about keeping his world of dance true and relevant. As I go in to coach at the Royal Ballet today, I think of him so fondly and try to follow his example."
A former welder, Goodman became a dancer on the advice of his doctor and never looked back.
After winning the British Championships in his 20s, he became a dance instructor and joined Strictly for its launch in 2004.
Popular with viewers for his wry humour and avuncular critiques, he managed to turn the act of giving scores into a source of catchphrases: From his comedically elongated pronunciation of "seveeeen" to the much sought-after "10 from Len".
Strictly's longest-serving judge, Craig Revel Horwood, referenced that showmanship while paying tribute on Monday, describing Goodman as a "gorgeous colleague and dear friend".
"Len Goody Goodman is what I always called him and 'It's a ten from Len & seveeeeern' will live with me forever," he added.
Winkleman told BBC News: "There was nobody like him because he was so humble.
"He was adorable - on camera, off camera, and to everybody who took part."
Her co-host Tess Daly agreed that Goodman was "a beautiful man, genuine, warm and humble, who left an impression on everyone he met".
"I'll never forget the fun we had on set, his love and passion for dancing and that wonderfully cheeky smile lit up the screen," she said on social media.
Bruno Tonioli shared a picture of him and Goodman together, declaring: "There will never be anyone like you. You will always be my perfect 10."
Current head judge Shirley Ballas said that her "past teacher" was a "dance legend" and "a true gentleman" as well as a "shining star in the ballroom that everyone loved."Anton Du Beke, who was a dancer and judge on the popular celebrity dancing show, recalled having first met Goodman when he was just a young lad, as he was his dance judge.
Camilla, the Queen Consort, who danced with Goodman at a public engagement in 2019, was "saddened to hear the news", according to a Buckingham Palace spokesperson.
A spokesman for the Prime Minister Rishi Sunak described Goodman as "a great entertainer, a popular face on TV screens up and down the country".
"He will be missed by many and our condolences go to his friends and family," he added.
:: "You floated across that floor like butter on a crumpet."
:: "It was like watching a stork who'd been struck by lightning."
:: "You were like a chess master - you plotted your way around that floor. That was a mango of a tango. Delicious."
:: "For me, you can't waft enough."
Goodman made his final appearance on Strictly during the 2016 Christmas Day special.
He also served as head judge on Dancing With The Stars for more than 15 years, announcing his retirement in November last year saying he wanted to "spend more time with my grandchildren and family" in the UK.
He died on Saturday at a hospice in Tunbridge Wells, Kent, having had cancer, surrounded by his family.
A statement from his manager, Jackie Gill, on Monday described him as "a much loved husband, father and grandfather who will be sorely missed by family, friends and all who knew him."
He leaves his wife Sue Barrett, who he married in 2012, and his son, James, from a previous relationship.