Burke was born in Keokuk County, Iowa and moved to the Dakota Territory. After North Dakota was admitted to the union, he served in the state's House of Representatives in 1891 and in its Senate from 1893 to 1896. He served three terms (1907-1913) as a Democratic governor at a time when the North Dakota Republican Party had little practical opposition. He ran for the United States Senate in 1916 but lost. From 1913 to 1921 Burke was Treasurer of the United States, under President Woodrow Wilson. He later served as a justice of the North Dakota Supreme Court from 1924 until his death on May 14 1937. Burke County, North Dakota is named in his honor.