Woods was the son of James Albert and Cornelia Dixon Witherspoon Woods. He attended the Lawrenceville School in Lawrenceville, New Jersey, and the University of the South in Sewanee, Tennessee. He married the former Loti Moultrie Chisolm in 1953, and began his banking career at the Chemical Bank in New York City in 1954. He took two years off to serve in the U.S. Air Force from 1955 to 1957.
During his tenure, Woods led AmSouth's growth from $800 million to $18 billion in assets. He helped lobby to change Alabama banking regulations to allow out-of-state acquisitions, which AmSouth aggressively pursued once the changes were signed into law in 1981. Woods saw the company debut on the New York Stock Exchange and change its name to AmSouth. Woods retired in 1995 and was succeeded by Dowd Ritter as CEO.
Woods also served on the boards of the Alabama Power Company, Avondale Mills, the Protective Life Corporation and McWane Inc. He also served on the president's council at the University of Alabama and as a trustee of Miles College and Tuskegee Institute. He spent a years as "Executive in Residence" at the University of Montevallo in 1978–1979, and also chaired the Board of Regents at his alma mater, the University of the South.
Woods died in 2002. He was survived by his wife, Loti, two of their three daughters, and four grandchildren.
- "John W. Woods, 71, Former Chief of Bank." (November 14, 2002) Associated Press / The New York Times