He was educated at the Abbey Christian Brothers' Grammar School, Newry. He graduated from Queen's University Belfast in 1961 with a first class honours BA in History, and attended the Institute of Historical Research, in London from 1961 to 1962. He was awarded his PhD by Queen's in 1971 and an LLD honoris causa in 1975 for distinction in historical work. In 2007 Cosgrove obtained the Barrister-at-Law degree qualification from King's Inns but declined to take the statutory Irish exams needed to be called to the Bar by the Chief Justice of Ireland. He took legal action over the issue. Cosgrove is understood to be fluent in Irish but feels that the exam required by legislation passed in 1929 to be inappropriate in 2007. The law was changed to provide a system for Barristers to learn Irish as part of their studies.
- https://www.ucd.ie/t4cms/ucd_presidents_6_cosgrove_2005.pdf[bare URL PDF]
- Shortall, Eithne (9 September 2007). "Barrister set to challenge Gaeilge rule". Sunday Times (Ireland edition). p. 8. Retrieved 6 December 2021 – via Gale Academic OneFile.
- Oireachtas, Houses of the (13 December 2007). "Legal Practitioners (Irish Language) Bill 2007: Second Stage. – Dáil Éireann (30th Dáil) – Thursday, 13 Dec 2007 – Houses of the Oireachtas". www.oireachtas.ie.
- Book (eISB), electronic Irish Statute. "electronic Irish Statute Book (eISB)". www.irishstatutebook.ie.