Grout was born in Compton in the British Canadian Province of Lower Canada. He was the son of Josiah and Sophronia Grout. His parents, native Vermonters, returned to that state when he was six. He received his early education in the public schools and at Orleans Liberal Institute at Glover, Vermont. He was a student at St. Johnsbury Academy when the Civil War broke out, and he left to enlist.
Grout enlisted October 2, 1861, as a private in Company I, 1st Vermont Cavalry. He mustered in as 2nd Lieutenant, Company I, on October 21, 1861. He was promoted to first lieutenant on April 25, 1862, and captain on April 4, 1863. After participating in 17 battles, he was wounded on April 1, 1863 at the Skirmish at Miskel Farm against the Confederate partisan John S. Mosby, near Broad Run, Virginia, and was discharged due to his wounds on October 1, 1863. After the St. Albans Raid, he was commissioned captain, Company M, Vermont Frontier Cavalry, on January 10, 1865, and promoted to major of the regiment on March 22, 1865. He mustered out with the two Vermont companies on June 27, 1865.
Career in law and politics
After the war, he studied law in Barton with his brother, William W. Grout, a Civil War veteran and politician. Josiah Grout was admitted to the bar in December 1865 and in 1866 moved to Island Pond, where he was in charge of the Customs House for three years. His appointment included the districts of Newport and St. Albans. In October 1867, he married Harriet Hinman, daughter of Aaron and Nancy Hinman. In 1874, he moved to Chicago, and afterward to Moline, Illinois, where he was one of the supervisors of Rock Island County for two years. He returned to Vermont in 1880, where he took up farming, and raised some of the finest Jersey cattle, blooded Morgan horses and Shropshire sheep in Vermont. Grout represented Newport in the Vermont House of Representatives in 1872 and 1874, and Derby in 1884, 1886 and 1883. He was elected state Senator from Orleans County in 1892. In 1874, 1886 and 1888 he was Speaker of the Vermont House of Representatives. He was an Republican, serving as chief executive officer of the Republican Club at Derby, and was vice president of the Vermont League of Republican Clubs for four years, and one year its president. In 1888, he is listed in a business director as owning farms in Essex County,, in Caledonia County, 600 sugar trees, 50 cows, 30 young cattle, 60 sheep, breeder of regular Jersey and Ayrshire cattle. At the Republican State Convention on June 17, 1896, Grout was narrowly nominated as the party's candidate, received 339 votes compared to William W. Stickney's 336. He easily beat his Democratic opponent in the general election, J. H. Jackson, receiving 54,426 votes to Jackson's 14,855. Grout's term was highlighted by enhancement to the state's educational system, the establishment of the post of Vermont Attorney General, a visit to the Tennessee Centennial Exposition. The Spanish–American War broke out during Grout's term, and at the start of the war Grout tended the services of a regiment of infantry and a battery of six guns from the Vermont Militia, which was accepted by the federal government. On May 21, 1898, he dispatched a regiment of 47 officers and 980 men to the war. Due to the short duration of the war, however, the Vermont regiment saw no active service, and returned to the state on August 21, where it was reviewed by Grout at Camp Ethan Allen. In October 1898, Grout was succeeded by Edward Curtis Smith, son of one of Vermont's previous governors, J. Gregory Smith. Grout again represented Derby in the General Assembly in 1904. Grout died in Derby, and is buried in the Derby Center cemetery. His son Aaron H. Grout, served as Vermont Secretary of State from 1923 to 1927.