George Washington Morgan was born in Washington County, Pennsylvania, in 1820. At the age of sixteen, Morgan left Washington College where he was studying to enlist for Houston in the War for Texan Independence. He entered as a lieutenant and was quickly appointed to captain. After his service, Morgan enrolled in the United States Military Academy. He stayed only two years, however, and began studying law under his future partner, J. K. Miller, in Mount Vernon, Ohio. Morgan was admitted to the bar and became the prosecutor for Knox County. Morgan held his position until he resigned to enlist as colonel of the 2nd Ohio Volunteers in the U.S.-Mexico War. At only twenty-seven years old, Morgan was commissioned Colonel of the 15th United States Infantry. Morgan was wounded at the battles of Contreras and Churubusco, and was named brigadier-general for his "gallant and meritorious conduct."

In 1848, Morgan returned to civilian life in Mount Vernon, Ohio, where he farmed and practiced law. President Pierce appointed him consul at Marseilles in 1856, and he became minister to Lisbon two years later. Morgan resigned this post to take up arms for the Union in the American Civil War. He was appointed brigadier-general and given command of the 7th Division of Buell's Army of the Ohio, then a division in the Vicksburg campaign, and finally the XIII Corps. After battling illness and discontent with the policy of using African American troops, Morgan resigned from the service in 1863.

Morgan was elected to Congress in 1866, serving until he was unseated in 1868. He was elected the following year, and served until 1873. After leaving Congress, Morgan returned to his law practice in Mount Vernon. Morgan was married to Sarah H. Hall and fathered two daughters. He died in Fortress Monroe, Virginia, in 1893.