Born in Bowdon, Georgia, Adamson attended the common schools. He was graduated from Bowdon College in 1874. He studied law. He was admitted to the bar in 1876 and commenced practice in Carrollton, Georgia. He served as judge of the city court of Carrollton 1885-1889. Attorney for the city of Carrollton for a number of years. He served as delegate to the Democratic National Convention in 1892.
Adamson was elected as a Democrat to the Fifty-fifth and to the ten succeeding Congresses and served from March 4, 1897, until December 18, 1917, when he resigned. He served as chairman of the Committee on Interstate and Foreign Commerce (Sixty-second through Sixty-fifth Congresses). He was appointed on December 17, 1917, a member of the Board of United States General Appraisers (now the United States Customs Court) and served until January 20, 1928, when he resigned. He resumed the practice of law in Carrollton, Georgia. He died while on a visit in New York City, January 3, 1929. He was interred in City Cemetery, Carrollton, Georgia.