Wells was the son of Wesley W. and Rosa A. Mock Wells of Missouri. His parents both died in his third year and he was raised on his grandparents' farm and attended district schools. In 1891 he began his career as a clerk in a bank owned by his great uncle. Three years later he enrolled at Bethany College in Bethany, West Virginia. His uncle and benefactor died during his junior term and he returned to Platte City as assistant cashier at the Wells Banking Company. In 1899 he was made president of the Bank of Edgerton and married the former Hallie Hurst Jacob in 1900.
Wells left in 1902 to take a position as cashier of the Carthage National Bank, and moved on from there to take the same position at the Fort Worth National Bank in Texas in 1905. He was elected cashier of the Commercial National Bank of Houston in 1909, then vice president of the Union National Bank of Houston in January 1912. After one year there, he moved to the same role with the First National Bank of Houston. In October 1914 he was elected the first governor of the newly-created Federal Reserve Bank of Dallas. He left in February 1915 to accept the presidency of the First National Bank of Birmingham. In 1925 Wells was elected president of the American Bankers Association. President Calvin Coolidge appointed him as a financial adviser to the Cuban government.
Wells resigned from the presidency of the bank in 1930 to become chairman of its board of directors. John Persons succeeded his as president. During the Great Depression he presided over the Department of Public Welfare and served on the executive board of the Civil Works Administration.
In Birmingham Wells was a member of the Birmingham Country Club, Southern Club, Roebuck Country Club and Rotary Club of Birmingham. He served on the Board of Directors of the Birmingham Chamber of Commerce and chaired the Alabama Red Cross campaign for war funds during World War I. He was also a 32nd degree Scottish Rite Mason, a Knight Templar, and member of the Mystic Shrine.
After Wells' death his widow bequeathed their art collection and the funds used to build the first permanent home of the Birmingham Museum of Art. The Oscar Wells Memorial Building continues to serve as the main entrance to the museum.
- Federal Reserve Bank of Dallas (n.d.) "Oscar Wells". Federal Reserve History