Burgess studied at the Somerset House School of Design in that city. In 1849 he travelled to California to join the Gold rush. Having tried his hand at mining, he and his brother Hubert set up a jewelry shop in Sonora repairing watches and fashioning jewelry. George traveled extensively through the gold rush country chronicling his experiences through watercolors.
In 1853, he and Hubert traveled to Hawaii where George continued his watercolor painting and made drawings on stone in preparation for lithographed views of Hawaii, which were then printed by the lithographic firm Britton and Rey in San Francisco. After several years the brothers returned to California and George established a studio and embarked on a career as a professional artist. He made a living as a portrait artist, but remains best known for his paintings of the gold rush. He was a founding member of the San Francisco Art Association in 1871.
The Amon Carter Museum (Fort Worth, Texas), the Bancroft Library (University of California, Berkeley), the Honolulu Academy of Arts, the Oakland Museum of California (Oakland, California) and the Yosemite Museum (Yosemite National Park, California) are among the public collections holding works by George Henry Burgess.