Cellach was a native of Aughrim, County Galway, and head of his branch of the Ó Cellaigh clan of Ui Maine.
His father, Domnall mac Aodh Ó Cellaigh, was married to Catherine Burke, a daughter of Ulick Finn of Clanricarde.
Cellach's great-grandfather, William mac Melaghlin Ó Cellaigh, was the first of the family to be associated with Aughrim.
He was married to Julia Ní Cellaigh, daughter of Tadg Dubh of Gallagh.
An article of 1934 gave his pedigree as Cellach mac Domnall m. Aodh m. William m. Melaghlin m. William Buidhe m. Donoch Muimbreach m. Conchobhair m. Domnall m. Teige Tailtenn m. Conchobar Maenmaige.