He was most noted as the commander of the scouts for George Armstrong Custer in the Little Bighorn Campaign (of which he was the last of the surviving officers to die of natural causes) during the Great Sioux War, as well as receiving the Medal of Honor for his actions in a conflict at Drexel Mission following the Wounded Knee Massacre.

With the eruption of the latest round of the Sioux Wars in 1876, Varnum accompanied the 7th Cavalry as it proceeded overland from Fort Lincoln to the Yellowstone River, and then to the mouth of the Rosebud.

During the Little Bighorn expedition, Varnum and the Crow scouts in his unit and a few Arikaras discovered the location of a huge Indian village with hundreds of lodges.

In 1890, Captain Varnum commanded Company B of the 7th Cavalry at the Wounded Knee Massacre on December 29, against the aging Sioux Chief Big Foot and some 350 of his followers.

The following day, during the Drexel Mission Fight at White Clay Creek, his heroics helped ensure a safe withdrawal for his troops.

After leaving active service, Varnum was a professor of military science at the University of Maine, and from 1912, he served as a recruiting officer in the reserves.

He was recalled to active duty and promoted to colonel during World War I as finance and disbursing officer at Fort Mason, California.

[3] On July 24, 2024, U.S. Secretary of Defense Lloyd Austin announced a review of twenty Medals of Honor awarded for the Wounded Knee Massacre, including Captain Varnum's, although Varnum's award was, unlike the other nineteen soldiers listed for review, for actions at the Drexel Mission Fight on White Clay Creek the day after Wounded Knee.