Irish President Michael D Higgins said that the news of Mr Healy’s death “will have been heard with sadness by so many”.
“Shay’s talents extended across so many areas and continued, even when challenged by illness, into the modern decades,” said President Higgins.
“His approach to everything he did was original and conveyed with enthusiasm.”
From Sandymount in Dublin, he started his career in RTÉ as a trainee cameraman and went on to present music programmes, as well as light entertainment and comedy shows.
His Eurovision-winning song was What’s Another Year, sung by Johnny Logan in 1980.
Mr Healy was the presenter of Nighthawks, a late-night talk show which covered entertainment and current affairs.
In 1992, it aired an infamous interview with the former minister for justice Sean Doherty about phone tapping, which eventually led to the resignation of Charles Haughey as taoiseach (Irish prime minister).