Born in Norwich, Connecticut, Donnelly was ordained a priest on June 29, 1934, for the Diocese of Hartford. On November 9, 1964 Pope Paul VI appointed him as the Titular Bishop of Nabala and Auxiliary Bishop of Hartford. He was consecrated a bishop by Henry O'Brien, Archbishop of Hartford, on January 28, 1965. The principal co-consecrators were Vincent Hines, Bishop of Norwich, and John Hackett, Auxiliary Bishop of Hartford.[1] Donnelly was an ardent supporter of farm laborers and served as the chairman of the Bishop's Committee on Farm Labor.[2] He also spent 20 years on the Connecticut Board of Mediation and Arbitration with fifteen of those years as its chairman. He served as Hartford's auxiliary bishop until his death on June 30, 1977, at the age of 68.[3]