Meacham was born in Chattanooga, Tennessee to C.W.K. Meacham, an attorney, and Jean Ellis. He graduated from the University of Tennessee at Chattanooga with an A.B. in 1935 and Vanderbilt University with an LL.B in 1937. He married Jean Austin (a teacher and later dean at the University of Tennessee at Chattanooga) on February 12, 1940. He served in the United States Navy Reserve 1941-1945, attaining the rank of commander.

Meacham was an attorney in Chattanooga from 1937 to 1972, when he became a judge in the Chattanooga Municipal Court.

A grandson, Jon Meacham, is the editor of Newsweek and a Pulitzer Prize-winning historian.

Meacham wrote a Napoloeonic nautical trilogy set in India published by Little, Brown in the United States and Hodder & Stoughton in the United Kingdom. The hero of the books is Percival Merewether, an officer in the Honourable East India Company’s private navy, known as the Bombay Marine.

• The East Indiaman (1968) Set in 1806 - Merewether commands HEICS Rapid
• On the Company’s Service, (1971) Set in 1806-1807 - Merewether commands HEICS Rapid again, and serves as Commodore
• For King and Company, (1976) Set in 1807-1808 — Merewether commands HEICS Pitt as a senior captain