On the 5th of November 1915, George was born in Webster Groves, Missouri, but he grew up in Detroit, Michigan, where he graduated from Southeastern High School in 1933. Before going to the University of Michigan, George attended the Culver Military Academy in Indiana and while at the University of Michigan, he enrolled in their Reserve Officers Training Corps. Before graduating with a degree in mechanical engineering, he received a commission to Second Lieutenant in the US Army Reserve, which he resigned after graduating in order to join the US Marine Corps, also as a Second Lieutenant, on the 25th of June 1938.

George attended the Basic School one month later and his first assignment was on board the USS Boise, followed by the Marine Barracks at Quantico, Virginia, and then attended the Base Defense Weapons Course. He was promoted to First Lieutenant when he arrived at Pearl Harbor with the 6th Defense Battalion and had reported to Sand Island, part of the Midway Islands about 1,000 miles northwest of Pearl Harbor, on the 7th of September 1941. It was his actions three months later during the Japanese attacks that brought the US into World War 2 that would later earn him the Medal of Honor. The citation reads:

For distinguished conduct in the line of his profession, extraordinary courage, and disregard for his own condition during the bombardment of Sand Island, Midway Islands, by Japanese forces on 7 December 1941. 1st Lt. Cannon, Battery Commander of Battery H, 6th Defense Battalion, Fleet Marine Force, U.S. Marine Corps, was at his command post when he was mortally wounded by enemy shellfire. He refused to be evacuated from his post until after his men who had been wounded by the same shell were evacuated and directed the reorganization of his command post until forcibly removed. As a result of his utter disregard of his own condition he died from loss of blood.

On the 7th of December, sixteen Medals of Honor were awarded and George was the first Marine of the War to receive the honor and the only Marine on the 7th. Initially George was buried on Midway but was later moved to the Halawa Naval Cemetery, which was one of the first cemeteries in Hawaii specifically for those killed in the attacks and World War 2. Once the National Memorial Cemetery of the Pacific, also known as the Punchbowl, was established and began accepting interments (January 4th, 1949), George Ham Cannon was moved there, where he rests today: Plot C 1644. There is also a cenotaph in the Glen Cove Cemetery in Knightstown, Indiana with his parents: Section 9. His Medal of Honor resides in the Culver Military Academy and a destroyer escort, the USS Cannon (DE-99) was named in his honor in May of 1943.