Buchanan was born to Patrick C. and Margaret Graham Buchanan in Rich Valley, Smyth County, Virginia. He received an A.B. in 1856 and an M.A.
Patrick C. Buchanan, the father of the subject, was born in Rich Valley, Smyth County, Virginia. His son, Buchanan, earned his undergraduate degree from there in 1856 and later acquired a graduate master's degree.