Tom Cullivan was born in 1939 in the cathedral and county town of Cavan, 70 miles north west of Dublin in the Irish lakelands. He began playing the piano at an early age and had formal lessons locally until his mid-teens. The urge to compose came almost as early. Three influences, the Liturgical music of the Latin Rite, Irish Music (especially as contained in the great collections of Bunting, Petrie, Joyce etc.) and the piano music of the great romantic composers of the 19th and 20th Centuries, are the dominant ones on his own style. He has been described by one authority as "flying the flag for 20th Century Romanticism in Ireland".

He began working as a composer while studying for his degrees in History, Celtic Archaeology and Law at University College Galway, when he wrote the score for a student production of Synge's "Deirdre of the Sorrows" (1968). Shortly afterwards, he was invited by actor/writer Richard Byrne to act as musical director for Alan Simpson's production of Brendan Behan's "An Giall (The Hostage)" at Taibhdhearc na Gaillimhe - the Gaelic arm of the National Theatre based in Galway. In 1972, producer and director Sean Stafford commissioned a score from him for Criostoir Ó Floinn's "Se Duirt Polonious". Subsequently, Cullivan went on to compose scores for Taibhdhearc productions of "The Shaughran", "Mise Raifteiri an File", "Nano", "The House of Barnarda Alba" and "An Hairyfella in Ifreann". The author of the last-named play, Eoghan Ó Tuairisc, was impressed with Cullivan's score and asked the composer to work with him on a play which he was about to start. The play and the music grew together to become "Aisling Mhic Artain" which won the national drama prize, Duais an Oireachtais, in 1975 and which received its first production at the Peacock Theatre during the Dublin Theatre Festival of 1977.