He was educated at the Abbey Christian Brothers' Grammar School, Newry.[1] He graduated from Queen's University Belfast in 1961 with a first class honours BA in History,[1] and attended the Institute of Historical Research, in London from 1961 to 1962.[1] He was awarded a PhD by Queen's in 1971 and an LLDhonoris causa in 1975 for distinction in historical work.[1] 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.[2] He took legal action over the issue.[3] Cosgrove was understood to be fluent in Irish but considered that the exam required by legislation passed in 1929 to be inappropriate in 2007.[2] The Legal Practitioners (Irish Language) Act 2008 was enacted following his action, which provided for a system for barristers and solicitors to learn Irish as part of their studies.[4]