On December 20, 1968, Gaydos was ordained to the priesthood for the Archdiocese of Saint Louis by Bishop Francis Reh in St. Peter's Basilica in Rome.
Gaydos became pastor of St. Gerard Majella Parish in Kirkwood, Missouri in 1990, and vicar general of the archdiocese on February 14, 1996.
On June 25, 1997, Pope John Paul II appointed Gaydos as the third bishop of the Diocese of Jefferson City.
[5] In March 2002, it was revealed that the diocese had made a secret settlement of $125,000 in 1996 to a former seminarian who claimed by have been sexually abused by O'Connell in 1969 at the seminary.
David Clohessy had sued the diocese in 1991, claiming that Whitely, then a pastor at St. Pius X Parish in Moberly, Missouri, had sexually abused him.
[8] In 2017, Gaydos sent a letter of resignation to Pope Francis, asking for early retirement as bishop of Jefferson City for health reasons.