Wheeler's awards and decorations included the Army Distinguished Service Medal, French Legion of Honour (Commander), and honorary Order of the Bath (Companion) from the United Kingdom.

He was appointed to the United States Military Academy (West Point) in 1883, graduated in 1887, and received his commission as a second lieutenant of Field Artillery.

[3] Wheeler graduated from West Point in 1887 ranked fourth of 64 and received his commission as a second lieutenant of Field Artillery.

[6] Among his classmates who also became general officers were Frank Herman Albright, Marcus Daniel Cronin, Alexander Lucian Dade, James Theodore Dean, Charles S. Farnsworth, George Washington Gatchell, Charles Gerhardt, Herman Hall, Thomas Grafton Hanson, Mark L. Hersey, Ernest Hinds, Michael Joseph Lenihan, Ulysses G. McAlexander, Nathaniel Fish McClure, George Owen Squier, and Edmund Wittenmyer.

[3] In December 1895, Wheeler was assigned to the Watertown Arsenal in Massachusetts, and in 1896, he was posted to the Office of the Chief of Ordnance in Washington, D.C.[3] During his service with the Chief of Ordnance, Wheeler was in charge of design, manufacture and maintenance of materiel used in Coast Artillery fortifications during the Spanish–American War and Philippine–American War, and he was promoted to captain on July 7, 1898.

[3] While in command at Watertown, he created the Taylor System of Scientific Management, which was intended to bring efficiency to the process of artillery weapons and equipment design, testing, procurement, and fielding.

[3] In March 1917, Wheeler rejoined the office of the Chief of Ordnance with orders to establish a nitrogen manufacturing plant.

[3] In addition, he received the Legion of Honour (Commander) from France and the honorary Order of the Bath (Companion) from the United Kingdom.

General Wheeler initiated, organized, and developed the plans for the successful operation of the Supply Division in the Office of the Chief of Ordnance, which division received, transported, warehoused, issued, and maintained all items of ordnance stores and equipment manufactured and purchase for issue to the Army during the war.

[3] He was a member of the Sons of the American Revolution as a result of his descent from David Safford, a militia soldier from Vermont.

[3] Lentilhon Wheeler (1898–1926) was a West Point graduate and World War I veteran who died at age 28 after contracting tuberculosis.

[16] Zella Trelawney Safford Wheeler (1907–2004) was a graduate of Wellesley College and the wife of architect G. Seth Nichols.