Yager was born in Campbellsburg in Henry County, Kentucky. He earned bachelor's and master's degrees from Georgetown College in Kentucky, and a doctorate from Johns Hopkins University. Yager then became a professor of history, economics, and politics at Georgetown College while becoming active in politics. He served as President of Georgetown College from 1908 to 1913.

In 1913, President Woodrow Wilson, a fellow Democrat who had been a classmate of Yager's when both attended Johns Hopkins University, appointed Yager to the governorship of Puerto Rico. During Yager's administration, and with his support, the United States Congress adopted the Jones-Shafroth Act (also called Jones Act) of 1917, which conferred United States citizenship on Puerto Ricans.

Yager served as governor until Wilson's presidency expired. He was succeeded by Emmet Montgomery Reily, an appointee of President Warren G. Harding. Yager returned to Kentucky, where he died in Pewee Valley at the age of 83.

A collection of Yager's correspondence from his time as Governor is archived at the Filson Historical Society in Louisville, Kentucky and open for research.

• Huffman, Noah (2006), "Arthur Yager: President of Georgetown College (1908-1913) and Governor of Puerto Rico (1913-1921)", The Filson Newsmagazine, 6 (3), retrieved 2008-08-13.
• "Obituary: Dr. Arthur Yager; Served as Governor of Puerto Rico for 8 years After 1913", The New York Times, p. 25, December 25, 1941.
• Yager, Arthur (1919), Twenty Years of Progress in Porto Rico under American Administration, San Juan: Bureau of supplies, printing and transportation, OCLC 164791160.

• Yager Collection at Georgetown College
• Filson Historical Society Newsmagazine, Vol.6, No.3