He had been ill in hospital and died in the early hours of Monday morning.
Tributes have been pouring in for the bishop, who was from Ballyshannon, County Donegal.
The image of the then Fr Daly waving a handkerchief over one of the Bloody Sunday victims, was one of the most enduring images of the Troubles.
He was then a 39-year-old curate at St Eugene's Cathedral in Londonderry having been a priest in the city since June 1962.
He was appointed Bishop of Derry in 1974.
He was forced into full retirement in 1994 after he suffered a stroke but he continued in the role of chaplain to Derry's Foyle Hospice until February, 2016.
Bishop Daly made headlines in 2011 when he said there needed to be a place in the modern Catholic Church for married priests.
He addressed the controversial issue in his book about his life in the Church, A Troubled See.
Allowing clergymen to marry would ease the church's problems, he said.
The bishop received the Freedom of the City of Derry in 2015.
Bishop Daly was "an iconic figure in the civic and church life of Ireland", said Archbishop Eamon Martin of Armagh, the Catholic primate of Ireland.
"As the bishop who ordained me to the priesthood in 1987, I had huge admiration for Bishop Edward," said the archbishop.
"I shall always be grateful for his pastoral guidance, kindness and support."
"Bishop Edward will be remembered as a fearless peace-builder - as exemplified by his courage on Bloody Sunday in Derry - and as a holy and humble faith leader.
"Bishop Edward's bravery was also apparent in his lived conviction that violence from any side during the Troubles was futile and could never be morally justified."
Bishop Donal McKeown of Derry said: "Bishop Daly served, without any concern for himself, throughout the traumatic years of the Troubles, finding his ministry shaped by the experience of witnessing violence and its effects.
"Through this dreadful period he always strove to preach the Gospel of the peace of Christ."
Deputy First Minister Martin McGuinness said Bishop Daly was "a constant right throughout the course of the last 40 odd years in the city through the good times and bad".
"Bishop Daly was inherently a shy person, he was not someone who sought the headlines, but he was propelled into the headlines because of Bloody Sunday, as he tried to help Jackie Duddy, for that iconic image," said the Sinn Fein MLA.
"He was a bishop and priest who was very in tune with the local community."
Mr McGuinness said Bishop Daly was always very critical of the IRA and "anyone that was involved in the conflict".
Pat Hume, the wife of former SDLP leader John Hume, said Bishop Daly had been an "immense source of strength" to her family.
"He was such a wonderful communicator," she told the BBC's Evening Extra programme.
"He could communicate and let a person feel so, so special and let them feel he had time for them, even though he was an extremely busy man.
"He always gave that impression that he had time for people."
The retired Catholic Bishop of Derry, Dr Edward Daly, whose photograph became the iconic image of Bloody Sunday in 1972, has died aged 82.