Wood was born in rural Munfordville, Kentucky, the son of George Thomas Wood, an army officer, and Elizabeth Helm. He was an 1845 graduate of the United States Military Academy, finishing 5th in a class of 41. He was commissioned as a second lieutenant in the Army Corps of Engineers.

In 1846, Wood joined General Zachary Taylor's staff for a few months as the Mexican-American War erupted. He soon transferred at his request to U.S. 2nd Dragoons and was cited for valor at the Battle of Buena Vista in February of 1847. After the war, he served in a succession of cavalry postings on the open frontier in the American Old West. Wood traveled in Europe from 1859 until early 1861 on a leave of absence from the army.

During early days of the Civil War, Wood helped organize, train, and equip several volunteer regiments in Indiana. In October of 1861, he was promoted to brigadier general of Indiana volunteers. The following month, he married Caroline E. Greer of Dayton, Ohio.

Wood commanded a brigade in the Tennessee and Mississippi campaigns at the beginning of the war. He commanded a division in the Army of the Ohio, then in the Army of the Cumberland. Wood was wounded during the Battle of Murfreesboro in December of 1862. He suffered controversy at the battle of Chickamauga, where he was blamed for contributing to William S. Rosecrans' defeat. Rosecrans had ordered Wood (against Wood's futile protests) to move his division to another spot, opening up a huge gap in the Federal line. Confederate General James Longstreet's men poured through the hole and almost cut Rosecrans' army in two. Rosecrans was relieved of duty for his ill-timed order, although he blamed Wood for the fiasco.

Wood redeemed himself during the successful assault on Missionary Ridge and at the Battle of Lovejoy's Station, where despite a badly shattered leg, he stayed on the field encouraging his men. He commanded the IV Corps of the Army of the Cumberland at the Battle of Nashville, and pursued John Bell Hood's Confederates after the Union victory. In January of 1865, Wood received a promotion to the rank of major general in the volunteer army. After the Confederates surrendered, he was assigned to duty in Mississippi with the occupation army. Frustrated with administrative duty with the Freedmen's Bureau and the politics of Reconstruction, he retired from the service in June of 1868, having achieved the same rank in the regular army. His old war wounds prevented him from his desire of returning to active duty on the frontier.

He moved to Dayton and became active in the Grand Army of the Republic, a social organization for Union army veterans. He also served as a member of the board of visitors at the Military Academy. Before he died in 1906, Wood was the last survivor of his West Point class.