Griffiths became an accomplished coach after the end of his professional playing career in 1997, inspiring stars such as Stephen Hendry, Mark Williams and Mark Allen – and also regularly commentated on snooker for BBC Sport.
Three-time world champion and fellow Welshman Williams was among the first to pay tribute on social media, describing him as a “mentor, coach, friend, legend”.
Northern Ireland’s Allen added: “What a legend of a man, who helped shape my career and life both on and off the table. Absolutely heartbroken. He wasn’t just a coach, he was family.”
Dennis Taylor, who was beaten by Griffiths in the 1979 final, said he was “one of the nicest people you could ever wish to meet”.
“I managed to see Terry on Saturday, his son Darren brought me in to Llanelli hospital and we did a lot of reminiscing because we go back so far,” Taylor told BBC Radio Wales.
“He was a very, very special person and a brilliant snooker player and probably one of the best coaches snooker has ever had.
“He just loved snooker and he never changed.”
Matchroom Sport president Barry Hearn also paid tribute to a “great friend”.
“Terry Griffiths versus Sid Hood for the Southern Area Amateur Snooker title was my first ever event I promoted in 1974,” Hearn told BBC 5live.
“He was just the most fantastic person, the greatest dry sense of humour, a Welsh fanatic, he loved Wales more than anything else.
“I don’t think anyone had a bad word to say about Terry… the straightest, nicest human being you could ever meet and he was just his own man.
“He loved playing snooker, loved the Crucible, terribly proud to be world champion and just a total joy to have around, all over the world he was one of our greatest ambassadors.”
Speaking after beating Barry Hawkins 10-8 in the final of the UK Championship in York on Sunday, current world number one Judd Trump also paid tribute to Griffiths.
“It is very, very sad news,” said the 2019 world champion. “It is tough for the family and they have such a history in snooker.
“Terry was a witty guy. He was always very funny and quick, and a legend of the game. He was someone that, when I went to the Welsh Open he’d always come over and make a joke.
“I think because of the people that went to him you could tell he was a great coach. I had a good connection. It is incredibly sad news and a sad day for Welsh sport in general.”
BBC snooker presenter Jason Mohammad also added on social media: “So sad to hear this news tonight.
“Thank you Terry for putting Wales on the sporting map – for your elegant commentary, chats and warmth in studio.
“Will never forget how you welcomed me to the snooker family when joining the BBC TV team. Prayers with all family and friends.”