Dawes, who was also captain and later coach of Wales with great distinction, was remembered by his former international team-mate Gareth Edwards as "one of the giant figures" in the history of its national team.
His death was announced by Newbridge, Dawes's first club, who reported he had experienced "a period of ill health".
Dawes, a centre, won his first Wales cap against Ireland in 1964 and helped the team to Triple Crown successes in 1965 and 1969 prior to leading his country to a Five Nations Grand Slam in 1971.
A Dawes-led Lions squad landed a 2-1 success against the All Blacks in the same year, with the fourth match in the series drawn.
That is the only time New Zealand has lost a series against the touring Lions, which it beat 3-1 six years later, by which time Dawes was head coach.
Dawes coached a great Wales team from 1974 to 1979, helping it win the Five Nations championship four times in six years, landing four Triple Crowns in the same period and Grand Slams in 1976 and 1978.
He became president of London Welsh, which said his death was "a seismic loss" for all of rugby.
Fellow Welsh legend Edwards featured alongside Dawes in the Barbarians side that famously beat New Zealand 23-11 in Cardiff in 1973, when Edwards scored what many regard as one of rugby's greatest tries.
The perfect excuse to watch *that* try again...— BBC Sport Wales (@BBCSportWales) July 12, 2020
🎂 Happy Birthday to the rugby great who gave us this unforgettable moment- Sir Gareth Edwards. 🎉 pic.twitter.com/hvTWqsvJDF
"I can still hear Cliff Morgan in commentary say, 'Dawes, great dummy'," Edwards said. "That moment encapsulated John as he helped to set up a score that has never been forgotten.
"John was a fantastic captain and a great coach. He is one of the giant figures of Welsh rugby of any era."
In his tribute posted on the Welsh Rugby Union website, Edwards added: "John was always calmness personified on the field amid the chaos of international rugby. People don't understand how valuable it is to have someone like that on your side, someone who can see the bigger picture and calm everyone down.
Sir Gareth Edwards wrote that John Dawes was "not only a great playmaker; as a leader he exercised a huge steadying influence on the tearaways around him."— Welsh Rugby Union 🏉 (@WelshRugbyUnion) April 16, 2021
Here is Dawes's first Wales try on debut in Lansdowne Road, March 1964 - as reported by @BritishPathe. pic.twitter.com/bzsqEtqoQL
"He never went over the top about our success when he was coaching. He would calmly tell us when we gathered for the first time in a season that while we weren't a good team at that moment, by the end of the season we would be a great side."