Davidson was hired by Booker T. Washington as a teacher and assistant principal of the Tuskegee Institute from 1881.
Her mother was a free woman of color and her father, Elias Davidson, had been freed from slavery.
When Olivia was a child, her family left western Virginia because of its discriminatory treatment of free blacks.
Her sister, a dressmaker and milliner, relocated with her husband several times before they settled in the larger city of Columbus, Ohio.
In 1878 their brother Joseph was murdered by the Ku Klux Klan, at a time of violence to suppress black voting.
She also began teaching a group of Native American men who had been enrolled there as students after being released as prisoners of war from a United States fort in Florida.
Booker T. Washington, the postgraduate speaker at Hampton, contacted Davidson, asking her to help him develop the new Tuskegee Institute.
During her time at Tuskegee, she also helped raise funds for the school, both locally and through her contacts in the North.
Olivia Washington suffered exposure to the early morning cold and had likely already contracted tuberculosis.
Her health deteriorated and she died three months later of laryngeal tuberculosis on May 9, 1889, at Massachusetts General Hospital.