Moevs was born in La Crosse, Wisconsin, and served in the United States Army Air Forces as a pilot during World War II.
Moevs was a student of Walter Piston and Nadia Boulanger.
He received the Rome Prize (1952) and a Guggenheim Fellowship (1962).
In 1978 his Concerto Grosso was awarded the Stockhausen International Prize in Composition.
His papers, including unpublished scores and recordings, are held by the Rutgers Music Library.