Burke was born in Toledo, Ohio on the 17th of December, 1872 and shortly after joining the US Navy, he deployed to China in support of the Boxer Rebellion. It was his actions as a Machinist First Class that would earn him the Medal of Honor. The citation reads:

Served with the relief expedition of the Allied forces in China on 13, 20, 21 and 22 June 1900. In the presence of the enemy during this period, Hanford distinguished himself by meritorious conduct.

Burke Gaius Hanford received his Medal of Honor the following year and he died at the age of 55 on the 11th of April, 1928. He is buried in the Greenwood Memorial Park, in San Diego, California: Acacia Grave 1523.