George Washington Thornton Beck was born on June 26, 1856 in Lexington, Kentucky to Senator James B. Beck and Jane Augusta Washington Thornton. In 1877 he moved to Leadville, Colorado during the Colorado Silver Boom and then worked for the Northern Pacific Railway in the Dakota Territory in 1878 before moving to Sheridan, Wyoming Territory in 1879.

Beck, Horace C. Alger, and later investors, including William F. "Buffalo Bill" Cody, George Bliestein, Bronson Rumsey, and Nate Salsbury founded the Shoshone Land and Irrigation Company to build a canal and irrigate land in the Big Horn Basin. The partners claimed land under the Carey Act project, hoping to bring in settlers and profit by selling water rights. The investors utilized the celebrity of William F. "Buffalo Bill" Cody, naming the town they founded Cody, Wyoming as well as the canal, after him. As the most directly involved in the day-to-day operations, Beck lived in Cody, Wyoming and guided the town in its infancy.

Along with other business leaders, Beck was vital in founding The Cody Club, which would become The Cody Country Chamber of Commerce. There is a street named in his honor in Cody. From 1889 to 1890 he served as the last president of the Wyoming Territorial Council and was the Democratic nominee for Wyoming's first House election, but was defeated by Clarence D. Clark. He was elected to the territorial Senate and the Wyoming State Senate as a Democrat.

In 1901 he ran for mayor of Cody in its first mayoral election, but was defeated by Frank L. Houx. In 1902 he ran for mayor again and was elected and later that year ran for the Democratic nomination for the 1902 gubernatorial election and on August 7, 1902 he received the Democratic nomination for governor, but was defeated in a landslide by Governor DeForest Richards. He later served as a delegate to the 1904 and 1908 Democratic National Conventions. On December 2, 1943 he died in his home in Cody, Wyoming from a heart attack.