Hyde was born in Princeton, Missouri. He graduated from the University of Michigan in 1899. While at the University of Michigan he joined The Delta Upsilon Fraternity. He became a lawyer, was elected Governor of Missouri in the 1920 election, and served one term from 1921 to 1925. During his first month as Governor, Hyde recommended extensive reorganization of state government by regrouping responsibilities into a few departments. Later he served as the Secretary of Agriculture under President Herbert Hoover. He died in New York City following cancer surgery in 1947.
Some of his family members were also involved in politics. His father, Ira B. Hyde, was a representative from Missouri, and his brother, Laurance M. Hyde, was a chief justice of the Missouri supreme court. He died on October 17, 1947.