Burroughs was born on September 1, 1875, in Chicago, Illinois (he later lived for many years in the suburb of Oak Park), the fourth son of businessman and Civil War veteran Major George Tyler Burroughs (1833–1913) and his wife Mary Evaline (Zieger) Burroughs (1840–1920). His middle name is from his paternal grandmother, Mary Rice Burroughs (1802–ca. 70).
Burroughs was educated at a number of local schools, and during the Chicago influenza epidemic in 1891, he spent a half year at his brother's ranch on the Raft River in Idaho. He then attended the Phillips Academy in Andover, Massachusetts, and then the Michigan Military Academy. Graduating in 1895, and failing the entrance exam for the United States Military Academy (West Point), he ended up as an enlisted soldier with the 7th U.S. Cavalry in Fort Grant, Arizona Territory. After being diagnosed with a heart problem and thus ineligible to serve, he was discharged in 1897.