The BBC announced that Gordon, who retired last year after four decades with the corporation, had died.
Richard Burgess, head of BBC sports news and BBC radio sport, described him as "a true gentleman."
Gordon joined the BBC in 1972 and went on to become one of the most recognisable voices on radio, reading the results first on Radio 2 and then Radio 5 Live.
His delivery made it possible to predict whether the result had been a home win, away win or draw simply from the inflection.
He retired in July 2013 after having his larynx removed to treat throat cancer.
Tributes were quick to flood in. England goalkeeper Ben Foster tweeted: "Saturday afternoons checking Teletext and listening to the footy scores was the best."
BBC pundit and former Wales player Robbie Savage said: "Such sad news, what a fantastic man with a great voice."