Born in Los Angeles, she grew up to attend the Manual Arts High School. After graduating, Arvey enjoyed a brief career as a concert pianist, including performances as a soloist with Raymond Paige's CBS Network orchestra and the Los Angeles Philharmonic Orchestra.
During a trip to Los Angeles in 1930 to revive a friendship with the composer Harold Bruce Forsythe, Still met Arvey, probably when Forsythe asked her to read some of Still's piano music. Still tried twice to get her to perform his pieces, first Africa, then Four Negro Dances. The two became more acqainted, but as Forsythe and Arvey had been friends for many years (since they had both gone to Manual Arts High School) some jealousy ensued.
Arvey married Still in 1939. Although Arvey was of Russian-Jewish heritage and Still was African American, their interracial union (unusual for a high-profile couple of the era) did not appear to damage their careers. The couple had two children and were married until Still’s death in 1978. 
Arvey’s first collaboration with Still came in 1939 when Langston Hughes, the original librettist for his opera Troubled Island, left the country before the project was completed. Arvey wrote the lyrics for three arias. She became the librettist for his subsequent operatic work, most notably A Bayou Legend, A Southern Interlude, Costaso and Mota. 
As a writer, Arvey produced articles for The New York Times and several music industry publications including Etude, Musical Courier, Opera, Concert and Symphony, Musical America, Chesterian (London), American Dancer, Ritmo (Madrid), Musical Digest and American Mercury. She wrote the 1939 monograph "Studies of Contemporary American Composers: William Grant Still," the 1941 book Choreographic Music, and the 1984 biography of her late husband, In One Lifetime.
- Smith, Catherine Parsons (2000). William Grant Still: A Study in Contradictions. University of California Press. ISBN 978-0-520-21543-6.
- "Verna Avery". William Grant Still Music & The Master-Player Library. Retrieved 2008-05-13.
- "William Grant Still Exhibition". Duke University. 1995. Retrieved 2008-05-13.
- William Grant Still Music, site with comprehensive information about him and his music
- Interview, Transcript, African American Music Collection, University of Michigan
- William Grant Still; Composer, Arranger, Conductor & Oboist Extensive info at AfriClassical.com