Born in Elsberry, Missouri, Cannon graduated from La Grange Junior College in Hannibal, Missouri in 1901, from William Jewell College in Liberty, Missouri in 1903, and from the law department of the University of Missouri at Columbia in 1908. He worked as a professor of history at Stephens College in Columbia, Missouri from 1904 to 1908. He was admitted to the bar in 1908 and commenced practice in Troy, Missouri.

In 1911 Cannon became a clerk in the office of the Speaker of the House. He showed much promise, and went on to work as the parliamentarian of the House of Representatives from 1915 to 1920, and the parliamentarian of the Democratic National Convention in 1920 (as he would again, forty years later). Cannon was elected as a Democrat to the U.S. House of Representatives, serving from March 4, 1923, until his death in Washington, D.C. in 1964. There he served as chairman of the Appropriations Committee.

Cannon was the author of "A Synopsis of the Procedure of the House (1918)," "Procedure in the House of Representatives (1920)," and "Cannon’s Procedure (1928)," subsequent editions of the latter being published periodically by resolutions of the House until 1963. He was the editor and compiler of "Precedents of the House of Representatives" by an act of Congress. He also served as regent of the Smithsonian Institution from 1935 to 1964. He is interred in Elsberry City Cemetery, Elsberry, Missouri.