In 1852 Burleigh moved to Kittanning, Pennsylvania. He became an Indian agent at Greenwood, Dakota Territory, and was elected as a Republican to the House of Representatives, serving from March 4, 1865-March 3, 1869. He was an unsuccessful candidate for reelection in 1868. He was a member of the Dakota Territorial council in 1877, then served as a contractor and in farming, and moved to Miles City, Montana 1879, where he practiced law.
He served as a member of the special session of the Montana Territorial council in 1887 and as a delegate to the convention that framed the constitution of Montana in 1889. He was a member of the first State House of Representatives, and served as prosecuting attorney of Custer County. He returned to South Dakota in 1893, serving in the State Senate. He resumed law practice, then died in Yankton, Yankton County, South Dakota. He was intered in in Yankton Cemetery.