In a statement his wife Eileen said the family was "heartbroken" but spoke of her hope for a "grand reunion".
The 88-year-old was the first First Minister of Northern Ireland and played a role in the peace process there.
He led the strongly Christian DUP and opposed successive deals including the Anglo Irish and Good Friday Agreements.
But in 2007 he entered government with Sinn Fein - after a career leading opposition to any deal with the IRA.
He had been ill for some time.
After his 1979 election to the European Parliament he caused controversy when he denounced Pope John Paul II as the "anti-Christ" in 1988.
He was known for several other attacks on the Catholic faith in Northern Ireland and at a loyalist rally in 1968 after attacks on Catholic homes he said: "Catholic homes caught fire because they were loaded with petrol bombs; Catholic churches were attacked and burned because they were arsenals and priests handed out sub-machine guns to parishioners".
His wife says he wanted his funeral to be private and attended only by the immediate family but a memorial service will be held later in the year.
Martyrs Memorial Free Presbyterian Church where Revd Ian Paisley preached
Archbishop of Canterbury Justin Welby said: "I would like to convey my condolences to Baroness Paisley and the family on the sad news today that Lord Bannside, Dr Ian Paisley, has died.
"He was a passionate advocate for his community, a parliamentarian who made his presence felt in our national life and a man of deep faith.
"History will remember him for many things but above all for having the courage, when he judged the moment to be right, of taking the difficult but vital steps towards reconciliation."
Director of the Evangelical Alliance in Northern Ireland, Peter Lynas, told Premier's News Hour he was a divisive figure in Northern Ireland.
He said: "He had spent time in prison, he had thrown snowballs at the Irish Prime Minister and he was known as doctor no.
"But he also had this huge positive impact on Northern Ireland and ultimately entering a power sharing executive with a Sinn Fein.
"So that's probably what he will end up being remembered most for."
Former DUP colleague and friend Jeffrey Donaldson told Premier's News Hour it will be devastating for Revd Paisley's family.
He said: "Our thoughts and prayers are with his wife Eileen and with his son Ian and family.
"His death at this time was unexpected and I'm sure they will be devastated at this passing.
"The entire community will rally round to support them at this time."
His deputy First Minster Martin McGuinness said: "I learned with deep regret and sadness of the death of former First Minister the Revd Dr. Ian Paisley.
"Over a number of decades we were political opponents and held very different views on many, many issues but the one thing we were absolutely united on was the principle that our people were better able to govern themselves than any British government.
"In the brief period that we worked together in the Office of the First and Deputy First Minister I developed a close working relationship with him which developed into a friendship, which despite our many differences lasted beyond his term in office.
"I want to send my sincere sympathy to his wife, Eileen, his children and extended family."
Ian Paisley and Martin McGuiness meet former US President George Bush
Mike Nesbitt, leader of the Ulster Unionist Party (UUP), said: "There will be plenty of time to reflect on Ian Paisley's impact on the shaping of the modern Northern Ireland and its relations with our nearest neighbours, but today is a time to give the Paisley household space to mourn.
"My sympathies to Baroness Paisley and the family."
Former Prime Minister Tony Blair said: "His religious beliefs were profound and genuine. He talked to me often about the need for forgiveness and I am sure part of what made him finally take the road to peace, was his capacity, driven by his Christian belief, to contemplate and then work for reconciliation.
"I don't suppose 40 years ago he would ever have thought that politically his life then would end as it does now. But I know he and Eileen would be very proud of his huge contribution to a peaceful future for Northern Ireland.
"My deepest condolences to all the family".
Sinn Fein president Gerry Adams said he was deeply shocked and saddened at Revd Paisley's death.
"There will be plenty of time for political analysis but at this point I wish to extend my deepest sympathies to Ian's wife Eileen and to the Paisley family at this very sad time," he said.
Speaking to BBC Radio 4's World at One Former SDLP leader Mark Durkan said: "He went from vicious rhetoric during the '70s to playing a virtuous role.
"The fact is that even though he absolutely opposed the Good Friday Agreement and all the agreements attempted before that, he ended up helping to seal the settled process that we now have, accepting power-sharing, North-South institutions and all the rest of it, and working in a good spirit."
He added Revd Paisley would be remembered as "someone who opposed initiative after initiative, who brought down various Unionist leaders and contributed to many lost years and lost opportunities, only in the end to accept things that he had always opposed, but actually to work within them with some grace".
Director of the Evangelical Alliance in Northern Ireland, Peter Lynas, speaking to Premier's News Hour:
Former DUP colleague and friend Jeffrey Donaldson speaking to Premier's News Hour: