Homer Adkins was born in Jacksonville, Arkansas. He attended Draughon's Business College in 1908 and graduated from the Little Rock College of Pharmacy in 1911 as a licensed pharmacist.
Adkins served in the United States Army during World War I as a Captain in the Medical Corps.
Adkins served one term as sheriff of Pulaski County, Arkansas and was the collector of internal revenue from 1933 to 1940.
In 1940 he was elected Governor of Arkansas. The Adkins administration presided over a doubling of the surplus in the state's treasury. His administration focused on highway construction and financing, electrification, worker's compensation. Adkins was reelected in 1942.
In 1948 he was appointed as administrator of the Arkansas Employment Security Division which is responsible for worker's unemployment insurance and other worker's claims.
In 1956 Adkins established a public-relations firm in Little Rock.
Homer Adkins is buried at the Roselawn Memorial Park Cemetery in Little Rock.