Appleby was born in Ash Grove, Greene County, Missouri to Andrew B. and Mary (Johnson) Appleby. He earned his A.B. from Grinnell College in 1913. He married Ruth Meyer on October 4, 1916. The couple had three children, Margaret Finley Appleby, Mary Ellen Appleby Sarbaugh, and L. Tom Appleby.
He began his career as a newspaper publisher in Montana, Minnesota, and Iowa from 1914 through 1920. He was the editor of Iowa Magazine in Waterloo, Iowa from 1920–1924 and an editorial writer at the Des Moines Register and Tribune from 1924 until 1928. The family moved to Virginia in 1928 where Appleby again worked as a newspaper publisher until accepting a position with the U.S. government. He served as the Executive Assistant to the Secretary of Agriculture from 1933 through 1940 and the Under Secretary of Agriculture from 1940 until 1944 in Franklin D. Roosevelt's administration. He was Assistant Director of the U.S. Bureau of the Budget from 1944 through 1947 in the Truman Administration.
He died in October 1963. His famous works include-Big Democracy(1945) Policy and Administration(1949) Morality and administration in Democratic Government(1952) Public administration for welfare state(1961)