Walsh is born at 11 Essex Quay in Dublin, the only child of Ralph and Mary Perce Walsh. His father is a watchmaker and jeweler. He inherits his sympathy for Irish nationalism and independence from his father, who has the boy enrolled in the Repeal Association before he is two years old. He is educated locally at Mr. Fitzpatrick’s School on Peter St. and at St. Laurence O’Toole Seminary School, Harcourt Street, Dublin. In 1856, he goes to the Catholic University of Ireland and three years later to St. Patrick’s College, Maynooth where he becomes Professor of Theology in 1867. He is appointed vice-president of Maynooth in 1878 and president in 1880. A poor preacher, he makes the press his pulpit, making a name for himself in the areas of land law and education.
Walsh is ordained into the priesthood on May 22, 1866. He is appointed Archbishop of Dublin on July 3, 1885 followed by his consecration on August 2, 1885. He serves in this position until his death in 1921 and is succeeded by Edward Joseph Byrne.
The Land issue divides the Irish hierarchy. Walsh supports agrarian reform on behalf of the rural population. He is openly sympathetic to Irish nationalism, and an advocate of both Home Rule and agrarian land reform. It is his support for this movement, led by Michael Davitt, which leads the Vatican to honour Michael Logue in Armagh with the dignity of Cardinal in 1893 rather than Walsh in Dublin.
Walsh serves on the Senate of the Royal University of Ireland (1883–84) and as part of the Commission of National Education (1885–1901). He is appointed Chancellor of the newly founded National University of Ireland in 1908, a position he holds until his death, after which he is succeeded by Éamon de Valera.