Richard Morrison was born at Midleton, Co. Cork, the son of John Morrison, also an architect. Originally intended for the church, he was eventually placed as pupil with James Gandon, the architect, in Dublin. He obtained through his godfather, the Earl of Shannon, a post in the ordnance department at Dublin, but this he abandoned, when he entered into full practice as an architect. Having resided for some time at Clonmel, where his son, William Vitruvius was born, he moved about 1800 to Dublin and settled at Bray, Co. Wicklow. He was a founder-member in 1839 and first vice-president of the Royal Institute of the Architects of Ireland. In 1793 he published Useful and Ornamental Designs in Architecture.
Morrison had very extensive public and private practice in Ireland. Among his public works were alterations to the cathedral at Cashel, the court-house and gaol at Galway, court-houses at Carlow, Clonmel, Roscommon, Wexford, and elsewhere. He built or altered very many mansions of the nobility and gentry in Ireland, and was knighted by the lord-lieutenant, Earl de Grey, in 1841. Morrison designed a number of works with his son, William Vitruvius, including Baronscourt, Co. Tyrone (from 1835), Kilruddery, Co. Wicklow, Ballyfin, Co. Laois and Fota, Co. Cork. He died at Bray on 31 October 1849, and was buried in Mount Jerome Cemetery, Dublin.