Blackburn was born about May 1761 in Frederick County, the youngest of nine sons and two daughters of Benjamin Blackburn and Mary Blackburn. The family moved to Virginia from Pennsylvania well before Blackburn’s birth, migrated to Augusta County in 1774, and subsequently moved to western North Carolina. Blackburn probably intended to go into the Presbyterian ministry when he entered Liberty Hall Academy (now Washington and Lee University). A brief interval of service in the army during the closing months of the Revolutionary War interrupted his education, but he received an AB from Liberty Hall in 1785. On August 18 of that year Blackburn married Ann Mathews, a daughter of George Mathews. Apparently accompanied by the newlyweds, Mathews soon moved from Staunton to Georgia, where he had begun acquiring land in Wilkes County in March 1784. Blackburn and his wife had no children of their own but adopted a son who died young.