The popular Cork-born man was the former director of family business Dunnes Stores and the owner of a chain of gyms.
He featured prominently in Irish life and was surrounded by controversy, with Taoiseach Leo Varadkar describing him as a “larger than life” figure who led “a life less ordinary”.
His son Robert said he would miss him in a way he could not describe, according to news site Extra.ie
“Overall, in the final analysis, he was a good and decent man.”
In 1981, Ben Dunne was kidnapped by the IRA and was released after seven days after a ransom was reportedly paid.
Payments Ben Dunne made to Irish politicians – including former taoiseach Charles Haughey – prompted the establishment of the McCracken Tribunal in 1997 and, subsequently, the Moriarty Tribunal.
In 2008, he apologised “unreservedly for the hardship and hurt” caused to a check-out worker Mary Manning, who led a strike at Dunnes Stores outlet on Dublin’s Henry Street against apartheid in South Africa during the 1980s.
He told RTE’s Liveline that he wanted to show that “as life goes on, even though wrongs were done, you can still overcome them and you can still be friends at the end of the day”.
Mr Varadkar said in a statement: “I was deeply saddened to hear that Ben Dunne has died. A constituent of mine in Castleknock and a local employer, I met Ben many times. He really was larger than life.
“Among other things, he pioneered the fitness industry in Ireland first with Westpoint and then Ben Dunne Gyms. He led a life less ordinary and in turn he made some mistakes in life.
“The best people do. He never allowed that to defeat him or hold him back. He touched the lives of tens of thousands who will mourn his loss.”
Sinn Fein leader Mary Lou McDonald said: “Very sad to hear of the sudden death of Ben Dunne.
“My thoughts are with his beloved family. He was a good man who cared about people. We will never see his likes again.”
Kenny Donaldson, director of Troubles victims’ group SEFF, said Ms McDonald’s comments were “quite astounding”.
He said: “We regret to learn of the death of Ben Dunne and offer our sympathies to his grieving family.
“Mary Lou McDonald’s comments are however quite astounding, zero reference to the Provisional IRA’s kidnap of him, nor the money they stole from the Dunne family in securing his release.”
The Department of Foreign Affairs said it was aware of the sudden death of an Irish citizen in Dubai and is providing consular assistance.