Eaton was born in Sutton, New Hampshire, and attended Thetford Academy in Vermont. He graduated from Dartmouth College in 1854, studied at Andover Theological Seminary, and was ordained in 1862 to the Presbyterian ministry.

Eaton served in the Union Army during the American Civil War. In November 1863, Maj. Gen. Ulysses S. Grant appointed him as the Superintendent of Negro Affairs for the Department of the Tennessee; there Eaton supervised the establishment of 74 schools. In 1863, Eaton was made colonel of the 63rd Regiment of Colored Infantry, and, in 1865, he was advanced to brevet brigadier general.

General Eaton edited the Memphis Post in 1866–1867. He was appointed United States Commissioner of Education in 1870 and served with great efficiency in the Bureau of Education. Commissioner Eaton also reorganized the Bureau of Refugees, Freedmen, and Abandoned Lands.

In 1886–1891, Eaton was president of Marietta College, and, in 1895, he was appointed president of Sheldon Jackson College in Sitka, Alaska. In 1898, he became inspector of education in Puerto Rico and played a role in the centralization of its educational system. His educational writings dealt largely with the education of freedmen. Eaton also wrote a history of Thetford Academy. He died in Washington, D.C.