Born near Salt Sulphur Springs, Virginia (now West Virginia), Harvey attended common schools in Indiana, Illinois, and Iowa. He became a civil engineer and moved to Kansas Territory in 1859, where he settled in Riley County and engaged in agricultural pursuits. From 1861 to 1864, he served with the Union Army during the Civil War, advancing to the rank of Captain in the Fourth and Tenth Regiments of Kansas Volunteer Infantry.

Harvey was elected to the Kansas House of Representatives, 1865-1866 and a member of the Kansas Senate in 1867-1868. He was Governor of Kansas from 1868 to 1872, and was elected as a Republican to the U.S. Senate to fill the vacancy caused by the resignation of Alexander Caldwell, where he served from February 2, 1874, to March 3, 1877. Subsequently, he was a government surveyor in New Mexico, Utah, Nevada, and Oklahoma, bfore returning to Kansas to resume agricultural pursuits. He died near Junction City, Kansas in 1894. Interment was in Highland Cemetery, Junction City.