Tannehill was born on July 14, 1874 in Dayton, KY. He broke into the National League at the age of 19 with the Cincinnati Reds; however, he struggled in 29 innings and did not reappear in the major leagues until three years later. After a partial season with the Pittsburgh Pirates in 1897, Tannehill, in 1898, set a career high in both innings pitched (3262⁄3) and wins (25). Tannehill had several good years with the Pirates until his career year in 1901, when he led the National League in ERA at 2.18. Tannehill posted an even better ERA in 1902––1.95––but as the league ERA had dropped even more precipitously, he did not lead the National League in ERA.
In his later years, Tannehill worked in a Cincinnati machine shop and was a frequent visitor to Crosley Field, the home of the Cincinnati Reds from 1912 to 1970. He died of a stroke at Speers Hospital in Dayton, Campbell County, Kentucky on September 22, 1956.