John Bleakley was born and died in Philadelphia, attending both the Academy and the College of Philadelphia. A lawyer, he was elected to the American Philosophical Society in 1789.
Bleakley was elected to the Board of Trustees of the University of the State of Pennsylvania in 1789, and after the union of that institution with the College of Philadelphia he continued as a trustee of the University of Pennsylvania from 1791 until his death in 1802.