Donnelly studied at the Christian Brothers School in Omagh and the Royal University of Ireland.
He was elected to Tyrone County Council in 1914, holding his seat until 1951, holding the post of council chairman from 1920 to 1924.
He was also a member of Omagh Urban District Council.
In 1916, he was a founder member of Sinn Féin in the county, alongside Cahir Healy, James McHugh and Basil McGuckin.
His seat was abolished in 1929, and he was instead elected for West Tyrone.