He was born in Dungarvan on 18 September 1828, son of Thomas Cleary (1792-1871) a merchant of Main Street and Margaret O'Brien (1800-1858). They had four other sons: Matthew, Michael, John and Rev. Patrick Cleary. James Vincent was educated at Salamanca and Rome. After his ordination in 1851 he obtained a degree of Doctor of Sacred Theology in 1862. He returned to Ireland where he was appointed professor of Dogmatic Theology and Biblical Exposition in St. John's College Waterford. In 1872 he was made President of the College. He was made Vicar General of the Diocese of Waterford in 1875. Father Cleary was appointed Dungarvan parish priest on 13 February 1876 and it was he who initiated the improvements to the Parish Church. Little had been done to the church since it had been built 48 years earlier in 1828. In October 1880 he was appointed Bishop of Kingston and was consecrated in Rome on 21 November 1880 by Cardinal Simeoni assisted by Dr. Croke, Bishop of Cashel, and Bishop George Butler of Limerick.

Cleary left Ireland on 16 March 1881 to take up his new appointment: From the time of his arrival in Kingston Bishop Cleary stood out as one of the great intellects of his time in Canada.

He re-built the Cathedral in Kingston and ordered a set of stained glass windows from the same company who supplied those for Dungarvan Parish Church. He died on 24 February 1898 aged 70 and was buried in a vault in the St. James Memorial Chapel. In his will dated 18 February 1898, he bequeathed $30,000 for the endowment of 3 chairs at Regiopolis College and $5,000 for a Scholarship Fund.