Radford etched his name in the history books with a thumping 85th minute equaliser for Hereford during their shock 2-1 win over Newcastle United in the FA Cup third round in 1972.
The goal, scored from 30-yards on a muddy Edgar Street pitch, is widely regarded as one of the competition’s greatest and sparked a pitch invasion that would go down in folklore.
Radford's goal also helped launch the career of John Motson - one of football's most well-known commentators - with the 26-year-old famously exclaiming: "Oh what a goal! What a goal! Radford the scorer... and the crowd are invading the pitch!"
Hereford, who came from 1-0 down to beat the Magpies in extra-time, became the first non-league team to beat a top-flight side since 1949.
"We are devastated to hear of Ronnie’s passing, and wish to extend our deepest condolences to his family and friends at this very sad time," a statement from Hereford read.
"Ronnie is not just a part of Hereford United folklore, he is a part of football history and has kept Hereford on the football map since 1972.
"His mild manner, and friendly and modest approach to life epitomised the man he was and he was always delighted to visit Edgar Street, to meet up with past teammates and watch the present day team in action.
"We will always keep Ronnie close to our hearts at Edgar Street, not just at FA Cup moments, but forever and celebrate him and his huge role in propelling Hereford United to the forefront of the nations attention with that goal and being part of that team."
"We will carry your spirit onwards. Rest in peace Ronnie."
Ricky George, who scored the deciding goal in extra-time for Hereford, posted a tribute on Twitter: "Ronnie Radford, a man with a heart as big as Wembley stadium.
"Ronnie’s name will be enshrined in FA Cup folklore forever. Love you top man", he added.