Born in Ohio, the son of a minister and his wife,[1] Dudley studied at Kenyon College, graduating in 1882,[2] before continuing to study law at Columbian University (now George Washington University), graduating in 1885; he was admitted to the bar that year,[3] and worked for the War Department.

[4] Three years later, in 1888, he moved to San Diego, California, where he was later elected a judge in 1890.

[4] A Republican,[4] Dudley was appointed United States Minister to Peru by President William McKinley on June 25, 1897;[5] he took up his post in September of that year.

[6] In December 1906,[7] McKinley's successor, Theodore Roosevelt, appointed Dudley to be United States Ambassador to Brazil,[8] a post he took up in April 1907.

Illness dogged Dudley and his wife during his career,[9][10][11] and would ultimately contribute to his death: after staying at Johns Hopkins Hospital for treatment of an unrelated complaint,[12] he died there of heart failure.