Burr attended primary school in the suburb of Kirkwood, and in September 1874 enrolled in Washington University, where he studied mining engineering.

Burr left the university in December 1877 and after receiving approval from Missouri Congressman Nathan Cole, enrolled in the United States Military Academy on July 1, 1878.

[1] Written above his portrait in the class yearbook was the name of Aaron Burr, third vice-president of the United States and his third cousin, three times removed.

He was assigned to the engineer battalion at Willets Point, New York from September 1882 to October 1884, receiving a promotion to first lieutenant in April 1883.

During his time in Portland, Burr supervised the construction of the Cascade Locks and had two sons, William Edward and John Green.

Burr was Assistant to the Engineer Commissioner of the District of Columbia for four years, during which time he made improvements to the capitol's water system, organized the planting of trees, and supervised construction of the Georgetown Reservoir.

He went on to serve several different assignments with the Corps of Engineers in New York, Pennsylvania, Georgia, Missouri, and Washington, D.C., and was promoted to major in January 1903.