He was 74.
No cause of death was specified but The Irish Independent said he had been in poor health since he suffered a stroke several years ago.
"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 statement from his family read.
"The presence of Seamus was a warm one, full of humor, care and courtesy -- a courtesy that enabled him to carry with such wry Northern Irish dignity so many well-deserved honors from all over the world," Irish President Michael D. Higginssaid .
Heaney, a former teacher, won the Nobel Prize for literature in 1995.
He is survived by his wife, Marie, and children, Christopher, Michael and Catherine Ann, the Independent said.