Mr Quigley was the chairman of Ulster Bank until 2001, and served for 10 years as a non-executive director on the main board of NatWest.
He also acted as an independent witness to UDA decommissioning.
It is believed he took ill during a service at Helen's Bay Presbyterian Church on Saturday morning.
First Minister Peter Robinson and deputy First Minister Martin McGuinness led the tributes.
"We offer our sincere and heartfelt sympathies to his family, friends and colleagues," the Stormont leaders said. "We were fortunate to meet Sir George on many occasions.
"His contribution to public service and the business sector was highly regarded and he played an important role in developing networks within our community that sought to seek a better understanding of each other's views.
"He was a strong advocate of mutual respect in building a cohesive and equal society."
Mark Durkan, Foyle MP, has known Mr Quigley for years both as a civil servant and in his various roles in the private sector.
"I am deeply saddened by the death of Sir George Quigley," said the SDLP politician.
"George Quigley was a man of energy, verve, compassion and humour. His warm instincts and sharp intelligence made him engaging and effective.
"I offer my sincere condolences to his family and friends at this very sad time."
Sinn Féin President Gerry Adams said: "On my own behalf and that of Sinn Féin I want to extend my condolences to his family, friends and colleagues.
"George was for many years a senior civil servant and then business leader. He was an experienced economist and was a long-time advocate of the all-Ireland economy."