George Wesley Atkinson was born in Charleston. After attending Ohio Wesleyan University, Mount Union College, and Columbia University, he returned to Charleston, where he served as postmaster from 1870 to 1876. After serving briefly as a United States revenue agent, he became editor of the Wheeling Evening Standard. From 1881 to 1885, Atkinson was the United States marshal for West Virginia. He established a law practice in Wheeling and was elected to Congress in 1888.
Despite the fact Atkinson was the first Republican governor in twenty-six years, his policies were similar to those of his Democratic predecessors. He advocated the growth of industry, improved transportation, funding for state institutions, and establishment of free public libraries. He was also the first governor to promote legislation to improve child welfare and labor conditions.
After his term as governor, Atkinson was actively involved with the work of charitable organizations and served as president of the Children's Home Society of West Virginia. He was the United States attorney for southern West Virginia from 1901 to 1905 and a member of the federal court of claims from 1905 to 1916. Atkinson was the author of numerous books about West Virginia. He died in Charleston in 1925.