The poet died in Cork on Thursday night after a short illness, according to the Irish Times.
Born in Belfast in 1941, Mr Mahon has mostly been resident in the Republic since his student days in Trinity College and had lived in Kinsale for the past several decades.
President Michael D Higgins paid tribute to Mr Mahon today, describing him as a "great poet".
The loss of Derek Mahon, yet another artist gone from us in recent times, is like the falling of oak trees.
He noted one of his poems, A Disused Shed in County Wexford, was in contention to be Ireland's favourite poem.
President Higgins said of Mr Mahon: "What I recall as his greatest strength was his poetic instinct to continually dredge for what was human about us; what was contradictory as well as what was full of possibility...
"The loss of Derek Mahon, yet another artist gone from us in recent times, is like the falling of oak trees. We are left with hope from the fruit of the acorns in which the writing and its encouragement represents as legacy.
"To his partner, family and many friends, Sabina and I send our deepest sympathy."
