Harvey Parnell was born at Orlando in Cleveland County, Arkansas. Parnell attended public schools and graduated from Warren High School in Warren, Arkansas. After graduating he worked as a bookkeeper and store clerk. Parnell took up farming in Chicot County, Arkansas.
Parnell became a member of the Arkansas House of Representatives from 1919 to 1921. He was elected to the Arkansas Senate and served from 1923 to 1925.
In 1927 he was elected to the post of Lieutenant Governor and the next year was elevated to the office of governor when John Ellis Martineau resigned from office to become a Federal judge. Parnell won election to the office in his own right in 1928 and was reelected to a second term in 1930.
The Parnell administration focused on establishing a state highway fund, creating a Bureau of Commerce and Industry, ugrading the school system. Henderson State Teachers College was also created during his administration. Parnell himself was a consistent supporter of women's suffrage and appointed Hattie Caraway to the United States Senate. Caraway would later win election for the office and become the first woman elected to the Senate.
The state's citizens blamed the incumbent Parnell for their situation as the Great Depression began and he left office in 1933 and returned to farming. He later worked for the Reconstruction Finance Corporation.
Harvey Parnell died in Little Rock, Arkansas. Parnell is buried at the Roselawn Memorial Park Cemetery in Little Rock.