Hartnett was born in Croom, County Limerick. Although his parents' name was Harnett, he was registered in error as Hartnett on his birth certificate. In later life he declined to change this as his legal name was closer to the Irish Ó hAirtnéide. He grew up in the town of Newcastle West, also in County Limerick, spending much of his time with his grandmother in the countryside nearby. Hartnett claimed that his grandmother, Bridget Halpin, was one of the last native speakers to live in Co. Limerick, though she was originally from North Kerry. He claims that, although she spoke to him mainly in English, he would listen to her conversing with her friends in Irish, and as such, he was quite unaware of the imbalances between English and Irish, since he experienced the free interchange of both languages. When he began school, he claims that he was made aware of the tensions between both languages, and was surprised to discover that Irish as a language that was endangered, but was also, to him, taught as a contrived, rule-leaden entity, with little or none of the attraction that it held for him at home. He was educated in the local national and secondary schools in Newcastle West. Hartnett emigrated to England the day after he finished his secondary education and went to work as a tea boy on a building site in London.

Hartnett had started writing by this time and his work came to the attention of the poet John Jordan, who was professor of English at University College Dublin. Jordan invited Hartnett to attend the university for a year. While back in Dublin, he co-edited the literary magazine Arena with James Liddy. He also worked as curator of Joyce's tower at Sandycove for a time. He returned briefly to London, where he met Rosemary Grantley on 16 May 1965, and they were married on 4 April 1966. His first book, Anatomy of a Cliché, was published by Poetry Ireland in 1968 to critical acclaim and he returned permanently to Ireland that same year.

Back in Dublin, he worked as a night telephonist at the telephone exchange on Exchequer Street. He now entered a productive relationship with New Writers Press, run by Michael Smith and Trevor Joyce. They published his next three books. The first of these was a translation from the Irish, The Old Hag of Beare (1969), followed by Selected Poems (1970) and Tao (1972). This last book was a version of the Chinese Tao Te Ching. His Gypsy Ballads, a version of the Romancero Gitano of Federico Garcia Lorca (1973) was published by the Goldsmith Press.

In 1974 decided to leave Dublin to return to his rural roots and his relationship with the Irish language. He went to live in Templeglantine, just five miles from Newcastle West and worked for a time as a lecturer in creative writing at Thomond College of Education, Limerick.

In his 1975 book A Farewell to English he declared his intention to write only in Irish in the future, describing English as 'the perfect language to sell pigs in'. A number of volumes in Irish followed: Adharca Broic (1978), An Phurgóid (1983) and Do Nuala: Foighne Chrainn (1984).

Hartnett had started drinking heavily and his alcoholism contributed to end of his marriage. In 1984 he returned to Dublin to live in the suburb of Inchicore. The following year marked his return to English with the publication of Inchicore Haiku, a book that deals with the turbulent events in his personal life over the previous few years. This was followed by a number of books in English including A Necklace of Wrens (1987), Poems to Younger Women (1989) and The Killing of Dreams (1992).

He also continued working in Irish, and produced a sequence of important volumes of translation of classic works into English. These included Ó Bruadair, Selected Poems of Dáibhí Ó Bruadair (1985) and Ó Rathaille The Poems of Aodhaghán Ó Rathaille (1999). His Collected Poems appeared in two volumes in 1984 and 1987 and New and Selected Poems in 1995. Hartnett died from Alcoholic Liver Syndrome. A new Collected Poems appeared in 2001.