Meigs was born in Washington, D.C., into a family with an impressive military pedigree. He was the oldest son of Maj. Gen. Montgomery C. Meigs and Louisa Rodgers Meigs and the grandson of United States Navy hero Commodore John Rodgers (naval officer, War of 1812). He was the great-great grandson of Return J. Meigs, Sr.
In 1859, he received an appointment to West Point, where he excelled in science and mathematics. He took a leave of absence to serve as an aide-de-camp to Philip H. Sheridan during the First Battle of Bull Run. After returning to West Point, he graduated first in his class in 1863, becoming a Second Lieutenant of Engineers.
After participating in the pursuit of the Confederate Army following the Battle of Gettysburg, he served on the staff of Brig. Gen. Benjamin Franklin Kelley in West Virginia, and he fought at the Battle of New Market and campaigned in Major Generals David Hunter's and Sheridan's operations in the Shenandoah Valley. Sheridan appointed him his Chief Engineer in August 1864 and had him brevetted captain and major for gallantry at the battles of Opequon and Fisher's Hill.
On October 3, 1864, a rainy night, Meigs and two Union soldiers were traveling on the Swift Run Gap Road to headquarters in Harrisonburg, Virginia, when they overtook three Confederate cavalrymen. Meigs called them to a halt, and one of the Confederates demanded that Meigs and his men surrender. The men briefly exchanged gunfire, during which Meigs was shot and killed. One enlisted man was taken prisoner and the other escaped and told Sheridan that Meigs, without an opportunity to defend himself, had been killed in cold blood. Furious in his belief that Meigs had been murdered, Sheridan ordered the town of Dayton, Virginia, burned to the ground. However, Sheridan later rescinded the order upon receiving news that it had been a fair fight, but not after having burned nearly thirty houses and barns.
Mainly because he was from a prominent military family, Meigs' death became a source of news and controversy. Believing his son had been murdered, Montogomery Meigs placed a reward of $1,000 on the killer's head. He hired a private detective to investigate, which investigation continued after the conclusion of the war.