He studied theology at Drew Theological Seminary and graduated in 1890. Welch joined the New York conferance of the Methodist Episcopal church, and from 1892 to 1893, he was pastor of St. Luke's Church. In 1905, he was appointed as President of OVU, and under his leadership at Ohio W.U., "may fairly be said to have entered upon a new epoch".
During 1907-1908, Welch served as President of the Association of Ohio College Presidents and Deans. Welch was also the President of the Methodist Social Service from 1909-1912, and later served as chairman of the Methodist Commission for Overseas Relief, 1940-1948.
He was concecrated a Bishop in 1916 and served in that capacity for 53 years until his death at the age of 106 in 1969.