Woodward was the grandson of pioneer Birmingham industrialist Stimpson Harvey Woodward, and the son of J. H. Woodward (1843-1917). After attending school at the University of the South at Sewanee, Tennessee and at the Massachusetts Institute of Technology, Woodward returned home to Woodward in western Jefferson County to work in the family business. He began as a general superintendent in 1899, became vice president by 1905 and president in 1910. By 1917, he became chairman of the Board of Directors. He also held directorships at Wheeling Steel Corporation, First National Bank of Birmingham, Seaboard AirLine Railroad, the Atlanta, Birmingham & Atlantic Railroad and the Children's Hospital of Birmingham. He also served as vice president of the Industrial Savings Bank. In 1904, he married Annie Jemison, daughter of Robert Jemison, Jr. They had five children: Eugenia (1905–1990), Martha, Anne, Joseph II (1912-1965) and Allan, Jr (1918-1987).
 Birmingham Barons and Rickwood Field
Woodward purchased a majority share of the Birmingham Coal Barons baseball team from J. William McQueen in 1909 while he was still in his 20s. Immediately he began planning a grand showplace for his new team. He contacted Connie Mack for advice on the details, including the field dimensions. He settled on Forbes Field in Pittsburgh and Shibe Park in Philadelphia (later renamed Connie Mack Stadium) as the models for the new park. He purchased land in the West End neighborhood of Birmingham from the Alabama Central Railroad. The $75,000 structure was designed by Southeastern Engineering Company of Birmingham (a short-lived subsidiary of Pittsburgh's General Fireproofing Company) and completed during the summer of 1910. The 12.7 acre park was flanked along the basepaths by concrete and steel stands. A tile-roofed cupola on the roof behind home plate provided space for the announcer and the press. Woodward named the field after himself, using his nickname and the first part of his last name.
- Moore, Albert Burton (1927) "History of Alabama and Her People". Chicago: The American Historical Society, Inc., Vol. 3; Guy Matlock, editor and compiler.
- "Who’s Who in Alabama." Birmingham: Dubose Publishing Co., 1940.
- "Who Was Who in America", 1960, Vol. III, IV
- Woodward Family Papers, Hoole Special Collections, University of Alabama, accessed June 16, 2008.