The Archive arose directly from a proposal to the Arts Council/ An Chomhairle Ealaíon in 1987 made by Harry Bradshaw and Nicholas Carolan to preserve historic sound recordings of Irish traditional music. These had been been uncovered during their production of the RTÉ radio series 'The Irish Phonograph' (1983–86).

The Council, which had earlier made a decision in principle to establish an archive of Irish traditional music, on the recommendation of a committee chaired by Breandán Breathnach, accepted the proposal. It appointed a Board to oversee its operations, and funded it first as a pilot project and then on an ongoing basis. Important additional revenue funding was later received from the Arts Council of Northern Ireland. 

The remit of the Archive has expanded over the years in line with its founding aims, and staff numbers have grown considerably. Staff have archival, library, audiovisual-recording, music engraving, administrative, digitisation, IT and other skills, and are themselves singers, musicians and dancers. 

While its chief documents are still sound recordings, it has become a multimedia archive with substantial holdings of printed materials, still and moving images, artefacts, etc. 

The Archive was first situated in Eustace St, Dublin, and moved to larger premises in 63 Merrion Square, Dublin, in 1991. On 15 November 2006 it opened in a permanent home at 73 Merrion Square. It holds there the largest collection of Irish traditional music in existence, and the largest collection of information on this tradition. It is now a premier centre for enjoying and studying this music.