Born in Cincinnati, Ohio, on January 22, 1852, Joshua Willis Alexander moved to Missouri to attend local schools. He earned a B.A. from Christian University (now Culver-Stockton College) in 1873. He later studied law and was admitted to the Missouri bar in 1875, setting up a law practice in Gallatin, Missouri.

After working in public administration and serving as president of the Gallatin Board of Education, Alexander became a member of the Missouri House of Representatives, leading it as Speaker in 1887. After a stint as mayor of Gallatin (1891-1892), Alexander became judge of the Seventh Judicial Court of Missouri from 1901 to 1907.

He then became a member of the U.S. Congress, serving in the House of Representatives from 1907 to 1919. Following the sinking of the Titanic, Alexander became the American delegate to the International Conference on Safety of Life at Sea.

President Woodrow Wilson appointed Alexander secretary of commerce after William Redfield resigned that post in December 1919; Alexander would carry on as commerce secretary until the end of the Wilson administration. He returned to Gallatin to practice law in 1921, becoming a delegate-at-large to the Missouri State Constitutional Convention in 1922. Joshua Alexander died on February 27, 1936.