William Wallace Grout attended St. Johnsbury Academy and graduated from the State and National Law School in Poughkeepsie, New York in 1857.
In 1857 William Wallace Grout was admitted to the bar and began practice in in Barton, Vermont. He served as Lieutenant Colonel of the Fifteenth Regiment, Vermont Volunteer Infantry, in the Union Army during the Civil War. In 1864 he attained the rank of Brigadier General as commander of one of three brigades organized for border defense by the Vermont State Legislature, at time of St. Albans raid.
Grout served as State's Attorney of Orleans County in 1865 and 1866. In 1868 he was a delegate to Republican National Convention from Vermont. He served in the Vermont House of Representatives from 1868 until 1870 and in 1874. In 1876 he was a member of the Vermont State Senate and served as President pro tempore.
He was elected as a Republican candidate to the Forty-seventh Congress, serving from March 4, 1881 until March 3, 1883. He was an unsuccessful candidate for reelection in 1882 to the Forty-eighth Congress.
Grout was elected to the Forty-ninth and to the seven succeeding Congresses, serving from March 4, 1885 until March 3, 1901. He served as chairman of the Committee on the District of Columbia in the Fifty-first Congress, and was on the Committee on Expenditures in the Department of War in the Fifty-fourth through the Fifty-sixth Congresses. After leaving Congress, he engaged in agricultural pursuits and the practice of law.
In 1860 William Wallace Grout married Loraine M. Smith. They had two children who died while in infancy. Loraine died in 1868.