The distinguished writer's family released a short statement after he passed away on Friday morning, having suffered from ill health in recent years.
He had still been making public appearances and recently performed at the Fleadh in Derry.
"The death has taken place of Seamus Heaney. The poet and Nobel Laureate died in hospital in Dublin this morning after a short illness," the family said, via his publisher.
Faber and Faber went on to express sorrow at the loss of one of the world's greatest writers.
"His impact on literary culture is immeasurable," a spokeswoman said.
"As his publisher, we could not have been prouder to publish his poetry over nearly 50 years. He was nothing short of an inspiration to the company, and his friendship over many years is a great loss."
While Seamus Heaney moved to Dublin in the 70s, he was born near Castledawson in Co Londonderry on 13 April 1939.
His first book Eleven Poems was published in 1965 for the Queen's University Festival, with his first major collection Death of a Naturalist following a year later.
Throughout his career as a writer, he has achieved critical acclaim and numerous prestigious awards - not least the Nobel Prize for Literature in 1995.
"It's like being a little foothill at the bottom of a mountain range, you hope you just live up to it," the poet said at the time.
Back in 2009, Seamus Heaney unveiled the threshold stone of the new Lyric theatre, branding the rejuvenation "a reminder of the vital artistic achievement in the past and the promise of ongoing creative vigour in the future".
Following news of his death, the poet's name was soon trending worldwide on Twitter.
Both his stunning work and his life were a gift to the world.
Bill and Hillary Clinton
Belfast poet and friend of Seamus Heaney, Michael Longley, said he felt as if he had lost a brother.
"I think there are tens of thousands of people today who will be feeling personally bereaved because he had a great presence," he said.
"Just as his presence filled a room, so his marvelous poems filled the hearts of generations of readers."
Sinn Féin deputy First Minister Martin McGuinness lead the political tributes to the literary giant.
"Not only was he a great poet, and a much admired Nobel Laureate, he was very much a great human being," he said.
"Only last week, I spent some time with Seamus following his performance at the Fleadh Cheoil na hÉireann in Derry and enjoyed a great conversation with him.
"He will be sadly missed, not just across Ireland, but also further afield where his work resonated with many people over many decades."
DUP First Minister Peter Robinson added: "Seamus made a significant contribution to literature, not just in Northern Ireland, but across the world.
"His legacy and love of literature is something that will inspire future generations."
Irish Taoiseach Enda Kenny said it would take Seamus Heaney himself to describe the depth of loss that would be felt over his death.
"He is mourned - and deeply - wherever poetry and the world of the spirit are cherished and celebrated," he said.
The presence of Seamus was a warm one, full of humour, care and courtesy – a courtesy that enabled him to carry with such wry Northern Irish dignity so many well-deserved honours from all over the world.
Irish president Michael D Higgins
Northern Ireland Secretary of State Theresa Villiers added: "Seamus was undoubtedly one of the greatest literary voices the island of Ireland has ever produced and a great ambassador for Northern Ireland.
"It is some consolation that his spirit will live on through his legacy of work and that future generations will continue to be inspired by his distinctive poetic voice."
Nobel peace laureate John Hume expressed sadness for the loss of his lifelong friend.
"His poetry expressed a special love of people, place and diversity of life," he said.
"That profound regard for humanity has made his poetry a special channel for repudiating violence, injustice and prejudice, and urging us all to the better side of our human nature.
"I have always received great inspiration from his written word and I am deeply grateful for the personal encouragement that I always received from such a warm friend and a wise man."
Ulster Unionist Party leader Mike Nesbitt hailed Seamus Heaney's global significance and artistry.
"His influence ran broader than the arts," he said.
"We all remember how President Bill Clinton chose Heaney's great phrase about when 'hope and history rhyme' from Heaney's play Cure at Troy in his speech in Londonderry, and went on to use it for the title of his book detailing his vision of the USA in the 21st century."
Bill Clinton's daughter Chelsea was among those worldwide who expressed sadness on Twitter, adding: "No doubt I am among many grateful for his life and words."
On Friday night the former US President Bill Clinton praised Heaney as "our finest poet of the rhythms of ordinary lives" and a "powerful voice for peace".
Mr Clinton and his wife Hillary said they were saddened to learn of the death of their "good and true friend".
"His mind, heart, and his uniquely Irish gift for language made him our finest poet of the rhythms of ordinary lives and a powerful voice for peace," they said.
"We loved him and we will miss him. More than a brilliant artist, Seamus was, from the first day we met him, a joy to be with and a warm and caring friend - in short, a true son of Northern Ireland.
They added: "His wonderful work, like that of his fellow Irish Nobel Prize winners Shaw, Yeats, and Beckett, will be a lasting gift for all the world."
Walk on air against your better judgement.
Seamus Heaney, 1939-2013
Acting Vice-Chancellor of Queen's University, Professor James McElnay, sent sympathies to the family on behalf of the whole university.
"Seamus was not only a former student, professor and honorary graduate of Queen's, but also a true friend of the university," he said.
"Seamus's contribution to the world of literature has introduced millions of people around the globe to the enjoyment of poetry and enhanced it for many more.
"At Queen's, he was generous not only with his scholarship, but also with his time, and we will miss his warmth, humour and brilliance."
The Most Revd Dr Richard Clarke, Archbishop of Armagh and Primate of All Ireland, also paid tribute to Seamus Heaney - having enjoyed one of his poetry readings just two weeks ago.
"By any standards, he was one of the greatest poets writing in the English language of our time," he said.
"A man with a great generosity of spirit, his poetry illuminated aspects of Irish life North and South which perhaps many of us would not have understood without his writing."
Seamus Heaney is survived by his wife Marie and children Christopher, Michael and Catherine Ann.
His funeral is expected to take place in Dublin on Monday before he is laid to rest in his native village of Bellaghy.
A book of condolence will be opened at Belfast City Hall on Monday morning, while one is available at Derry's Guildhall.
"His words spoke of love, memory, past and present, conflict, the world and it was his interpretation of English language that touched the hearts and minds of many", the city's Mayor Martin Reilly said.