Matthews, who toured Australia and New Zealand with the Lions in 1950, making 20 appearances, was part of a legendary midfield partnership with Bleddyn Williams.
He was also the Lions team doctor on the 1980 tour of South Africa and famously shared a draw with Rocky Marciano while the boxer was stationed with the US Army in Wales.
WRU president Dennis Gethin led the tributes to the 17-cap tough-tackling centre:
"He will go down in Welsh rugby history as one of the greatest ever. He was renowned for his devastating tackling, not just in Wales but around the world.
"His partnership with Bleddyn Williams was the stuff of legend."
Former Wales and Lions coach John Dawes:
"Of course Jack and Bleddyn set the world alight when they played together. That was my first recollection of Jack as a player.
"Swash-buckling, uncompromising, devastating are all such words…powerful and aggressive.
"He took no prisoners yet was skilful and an international of some class."
Wales and Lions fullback JPR Williams:
"He was a great friend of my father's, they went to medical school together and my father used to play outside of Jack on the wing.
"We used to call him 'uncle Jack' and he gave me my first ever rugby ball, I remember it being a heavy leather one.
"He was a bit before my time as a player but my father would speak about him and he was renowned as a hard tackler.
"Jack was also an excellent boxer and anyone who goes three rounds with Rocky Marciano must have been tough. He will go down in folklore as one of Wales' all-time greats."
Cardiff Blues chairman Peter Thomas:
"Jack Matthews was undoubtedly one of the greatest centres Wales has ever produced and formed a formidable centre partnership with his great friend Bleddyn Williams.
"He was a strong runner, a devastating tackler and showed his class not only for Cardiff but also for Wales and the Lions.
"He was an outstanding player in the '40s and '50s for Cardiff before being appointed Chairman of the club. Our thoughts and prayers are with his family at this sad time."
Cardiff Medicals RFC coach Huw Davies:
"We were obviously very proud to have Dr Jack as one of our own. Jack and Bleddyn were a great double act. It was inspirational, really, for the modern students to sit in the company of two of our really, truly great players."