Roche was born in Wexford and was educated at Wexford Christian Brothers School and University College Dublin (UCD) where he received Bachelor of Commerce Degree and a Masters Degree in Public Administration. Roche's grandfather, Jem Roche, was a one-time heavyweight boxing champion of Ireland who also fought unsuccessfully for the world title.
Roche is married to Eleanor Griffin, and they have three sons and one daughter. They live in County Wicklow.
On 15 December 2008 he was held hostage during a robbery at the Druids Glen Marriott Hotel and Country Club in County Wicklow.
Roche worked as a public servant at the Departments of Posts and Telegraphs, Transport and Power, Finance and at the Department of Economic Planning and Development. In 1978 he was appointed lecturer in Public Administration and Public Finance at UCD. In 1978 Roche became the first Irish Citizen to be awarded a United Nations Human Rights fellowship. He subsequently became a member of the Irish Commission for Justice and Peace and served as a time as Chairman of the Commission.