Wilbur was born September 24, 1888 in Palmer, Massachusetts. He graduated from the United States Military Academy at West Point in 1912 and joined the Army from his birth city of Palmer, Massachusetts. He also attended the French military academy École spéciale militaire de Saint-Cyr as a classmate of Charles de Gaulle and saw combat in World War I. He served as chief of staff of I Armored Corps from 1941 to 1942.

On November 8, 1942 Wilbur, now a colonel, participated in Operation Torch, the Allied invasion of French North Africa. He served on the staff of Major General George S. Patton as part of the Western Task Force, charged with capturing the city of Casablanca, Morocco, from the Vichy French forces. Several American officers, including Wilbur, were chosen to carry messages to French commanders who were believed to be sympathetic towards the Allies. Wilbur was to contact Admiral François Michelier, commander of the French naval forces in Casablanca, and deliver to him a letter from General Patton. The Allies hoped to gain assistance from these French commanders, or at least convince them to lay down their arms and not oppose the invasion.

After landing with the first assault wave in Fedala, Wilbur approached the French lines under a white flag of truce and was escorted to their division headquarters. Finding that his intermediate contact there had been arrested for treason, he attempted to give the letter to the presiding general. The general refused to accept it, so Wilbur placed the letter on the man's desk and left. Before reaching his vehicle, he was stopped by another officer who offered to take him to Admiral Michelier. Upon arriving at the admiral's headquarters, he was turned away; Michelier refused to meet with him. Wilbur headed back to the American lines in Fedala.

After arriving back at the Allied-held beachhead, Wilbur led an attack against a French artillery battery. One of the few French guns still firing in the area, the battery was targeting Allied ships off shore. Wilbur gathered four tanks and a company of infantry to assault the position. He personally accompanied the group, riding along on the lead tank, and commanded them in the successful capture of the battery.

Wilbur was approved for the Medal of Honor two months later, on January 13, 1943. The medal was presented to him by President Franklin D. Roosevelt during a ceremony in Casablanca on January 22, 1943, in the midst of the Casablanca Conference. Also in attendance were General George Marshall, the Chief of Staff of the United States Army, and Major General Patton.

Wilbur continued to serve for the remainder of the war, rising to the rank of brigadier general. As deputy commander of the 36th Infantry Division during the Italian Campaign, he participated in the Allied landings in Salerno and the subsequent fighting through the winter of 1943-1944. He was then stationed in east Asia before retiring from the Army in 1947.

A strident anti-communist, Wilbur became involved in the political discourse regarding the Korean War. South Korean president Syngman Rhee had offered him an official advisory post before the war, but he declined the position. In 1950, his son, Army Lieutenant William H. Wilbur, Jr., was killed in Korea and posthumously awarded the Army's second-highest honor, the Distinguished Service Cross. Wilbur was a vocal supporter of then-Presidential candidate Dwight D. Eisenhower's plan to withdraw American troops from Korea, giving several speeches on the topic in 1952.

He was also involved in law enforcement, serving on the Chicago Crime Commission and briefly as warden of the Cook County Jail. He authored several non-fiction books, including The Making of George Washington (1973, ISBN 978-0912530024) and Freedom Must Not Perish (1964).

He died at age 91 and was buried in West Point Cemetery on the grounds of his alma mater, the U.S. Military Academy.

His official Medal of Honor citation reads:

For conspicuous gallantry and intrepidity in action above and beyond the call of duty. Col. Wilbur prepared the plan for making contact with French commanders in Casablanca and obtaining an armistice to prevent unnecessary bloodshed. On 8 November 1942, he landed at Fedala with the leading assault waves where opposition had developed into a firm and continuous defensive line across his route of advance. Commandeering a vehicle, he was driven toward the hostile defenses under incessant fire, finally locating a French officer who accorded him passage through the forward positions. He then proceeded in total darkness through 16 miles of enemy-occupied country intermittently subjected to heavy bursts of fire, and accomplished his mission by delivering his letters to appropriate French officials in Casablanca. Returning toward his command, Col. Wilbur detected a hostile battery firing effectively on our troops. He took charge of a platoon of American tanks and personally led them in an attack and capture of the battery. From the moment of landing until the cessation of hostile resistance, Col. Wilbur's conduct was voluntary and exemplary in its coolness and daring.