Born in 1827 on Screamer Mountain in Rabun County, Georgia, Bleckley became a self-taught lawyer.
Their son, Haralson Bleckley, became an architect and designed the University of Georgia Library Building built in 1904.
In 1857, Bleckley was elected to the office of Solicitor General in his judicial circuit covering eight counties and served in that capacity for the next four years while still maintaining his practice.
In 1861, Bleckley briefly joined the Confederate Army but was discharged for health reasons and returned to his law practice in Atlanta.
Bleckley died in Clarkesville, Georgia on March 6, 1907, and is buried at Oakland Cemetery in Atlanta.