He was educated in Christian Brothers Schools in Drogheda and Castleknock. Donegan was first elected as a Fine Gael TD in 1954. He lost his seat at the following election but reclaimed it in 1961. In the Fine Gael-Labour coalition of 1973 Donegan was appointed Minister for Defence.
In October 1976 Donegan made a contoversial speech on an official visit to a military base. He referred to President Cearbhall Ó Dálaighs refusal to sign tough anti-crime legislation as a 'thundering disgrace'. The Taoiseach, Liam Cosgrave, refused Donegan's resignation. Instead Ó Dálaigh resigned as President of Ireland. The whole episode badly damaged the governments reputation.