He was ordained to the priesthood, for the Diocese of Rochester, by Archbishop Martin O'Connor on December 15, 1957, at the chapel of the North American College.

[citation needed] In the capacity of Catholic chaplain, Moynihan served the Monroe County jail, Rochester police department (1962–1973), and Highland Hospital (1974–1976).

[citation needed] On April 4, 1995, Moynihan was appointed the ninth Bishop of Syracuse by Pope John Paul II.

He received his episcopal consecration on the following May 29 from John Cardinal O’Connor, with Bishops Joseph O'Keefe and Matthew Clark serving as co-consecrators.

Richard McBrien as a columnist for the diocesan newspaper, replacing him with the more theologically conservative writer George Weigel, much to the clergy's dismay.