The former leader of the Social Democratic and Labor Party (SDLP) had been ill for some time.
Having devoted his life to the pursuit of Irish unity by peaceful means, he has come under heavy criticism for having had secret talks with Gerry Adams.
But in 1993, Mr Hume persuaded the British and Irish governments that the weapon could be withdrawn from Irish politics.
When the IRA declared its ceasefire the following year, Sinn Fein was brought back from the political cold.
It was the start of a peace process that would culminate in the Good Friday Accord and the power-sharing government in Stormont.
In 1998, Mr. Hume and his Unionist counterpart David Trimble jointly received the Nobel Peace Prize.
Speaking at the award ceremony in Oslo, Mr Hume said: ‘I want to see Ireland as an example to men and women around the world of what can be achieved by living for ideals. rather than fight or die for them. ”
In a statement, his family said: “We are deeply saddened to report that John passed away peacefully in the wee hours of the morning after a short illness.
“We would like to express our sincere thanks to the caregivers and nurses at Owen Mor Nursing Home in Derry.
“The care they showed John during the last months of his life was exceptional. ”
They added, “John was a husband, father, grandfather, great-grandfather and brother. He was much loved and his loss will be deeply felt by all of his extended family.
“It seems especially fitting on these weird and frightening days to remember the phrase that gave John and so many of us hope through dark times: We will overcome. ”
Irish Prime Minister Micheál Martin described Mr Hume as “one of the greatest Irish people who ever lived” and said his life was an “impressive achievement”.
“John Hume was a great hero and a true peacemaker,” he said, adding, “All the inhabitants of this island will give thanks for his life. ”
The Prime Minister of Northern Ireland, Arlene Foster, has said he is a “giant of Irish nationalism”.
“In our darkest days, he recognized that violence was the wrong way and worked tirelessly to promote democratic politics,” the leader of the Democratic Unionist Party wrote on Twitter.
Writer and journalist Eamonn Mallie, who knew him well, said: “Hume was driven by one thing – a passion for peace. He hated this violence. He resented this violence.
“At each conference, constant at the North Star, Hume clarified, emphasized, amplified, the grotesque nature of what the IRA was doing. ”
Mr Hume had made a name for himself during the civil rights movement in his native Derry.
Member of Parliament for 22 years, MEP for 25 years, he became a dominant figure in Anglo-Irish politics of the 20th century.
Former US President Bill Clinton described him as ‘King Martin Luther of Northern Ireland’, while former UK Prime Minister Tony Blair said he made an ‘epic’ contribution to the peace process .
“John Hume was a political titan; a visionary who refused to believe that the future had to be the same as the past, ”said Blair.
SDLP leader Colum Eastwood MLA said: “Her legacy is Ireland at peace with itself. Its legacy is the end of 800 years of history and now allows us to realize all kinds of possibilities.
“We don’t fight with each other anymore and there is no way we will in the future.
“We are at peace, we have a democratic opportunity to define our own future. John Hume did. “