Born in Brooklyn, New York, Brady enlisted in the United States Army in 1965 and was decorated for his service in Vietnam. After leaing the Army, Brady serve as a special agent for the Bureau of Alcohol, Tobacco and Firearms. Brady studied at the University of Nebraska at Omaha, the City University of New York and earned his law degree from the California Western School of Law. In 1978, he began practicing law in Fayetteville, North Carolina.