The 49-year-old was found dead after collapsing while out for a walk on Monday night. It is believed he had suffered a heart attack.
The leading publican and hotelier was widely credited with the development of Dublin’s Temple Bar as a cultural and tourism hub.
However, the financial crisis of 2008 led to the collapse of his business empire with debts of over €250m.
Last July, Mr O’Regan was restricted from acting as a company director for five years by the High Court.
Chief mourners at the packed Star of the Sea Church in Sandymount were his wife Adrienne, four sons, Stephen, Adam, Alex, and Hugo, and his brothers Declan and Paul.
Fr Joe Kennedy, who presided over the concelebrated Mass, described Mr O’Regan as a visionary and perfectionist.
“There is some gathering of people here in Sandymount and Hugh would be greatly touched by the turn-out of so many friends, neighbours and colleagues,” he said.
Among them was RTÉ director general Noel Curran, businessman Ben Dunne, restaurateur Jay Burke, concert promoter John Reynolds, chef Dylan McGrath, rugby analyst Brent Pope, and fashion designer John Rocha and his wife Odette.
Fr Kennedy said he had known Mr O’Regan since the death of his brother Jack, 10 years ago.
He described him as a good man. “When he suffered a heart attack on Monday evening last as he was walking near Newtownmountkennedy, I have no doubt that Hugh was ready for his final journey back to the God who created him.”
Mr O’Regan’s son Stephen said his father had loads of dreams and “loads of them” had come true.
He became emotional as he revealed his father had helped Camera, a charity that uses technology in disadvantaged communities to improve education and livelihood skills.
He revealed 500,000 African children were using 35,000 reconditioned computers distributed by the charity.
Politician and writer Mannix Flynn said he had no doubt Mr O’Regan was in Heaven rearranging everything.
“Walls and doors are being ripped off. Everybody is running around with a hard hat and he is the one with a vision,” he said.
“One thing I am sure of is that when I pass away, Heaven will be ready for me. It will be hospitable; there will be a nice seat, a nice bit of grub, a lovely cup of coffee and a lend of a few bob.”
Mr O’Regan’s son Adam sung a moving version of U2’s ‘Kite’, containing the lyrics: “Who’s to say where the wind will take you; who’s to say what it is will break you.”