Claude Bolin Farrington attended Sam Houston Normal Institute and completed his education in 1893. In September of 1901, Farrington became a faculty member at SHNI for the Department of Chemistry. Farrington continued teaching chemistry as the institute changed its name to Sam Houston State Teachers College. He married Gladys Farrington.

In 1958 the new science building at SHSTC was named in honor of Claude Bolin Farrington, the Farrington Science Building or the Farrington Building. This new science building housed the Chemistry, Mathematics, and Physics Departments. Facilities within the building included laboratories, a planetarium, and a celestial observatory. In 1985 the observatory moved to Country Campus due to encroaching light from the expanding city and campus, and later in 1997, it moved off Highway 19 near Riverside.

Before the construction of the Farrington Building, science classes were held in the Science Building from 1916, moving the science classes from Austin Hall. The Science Building is now the Bobby K. Marks Administration Building (also known as the Marks Administration Building).

In 2002, the Board of Regents approved the funds for renovations and the construction of an addition to the building. Renovations to Farrington Building were initially reserved for the first floor. In 2004 the rest of the building was approved and completed in 2006. In 2003, the addition to Farrington was redesigned as a separate facility which became the Chemistry and Forensic Sciences Building located near Farrington. Construction started on March 28, 2004, and completed in September 2005.

The Farrington Pit receives its name by being close to the Farrington Building. It is the site of the original Education Building, which was removed in 1983 due to foundation issues.