Born in Vicksburg, Mississippi, Garvey graduated from St. Aloysius High School and worked for the Illinois Central Railroad.

He moved to Phoenix in 1940 when he was hired as assistant to Secretary of State Harry M. Moore.

Upon Moore's death in 1942, Garvey was appointed to succeed him by Governor Sidney P. Osborn, himself the first Secretary of State during most of the 1910s.

Garvey assumed the governorship, in accordance with Arizona law, when Osborn died on May 25, 1948.

[3] At the end of his elected term as governor, Garvey was appointed Arizona administrator for the federal Reconstruction Finance Corporation.