Madison, New Jersey. Madison is a borough in Morris County, New Jersey, United States. As of the 2010 United States Census, the population was 15,845, reflecting a drop in population of 685 (−4.1%) from the 16,530 counted in the 2000 Census, which had in turn increased by 680 (+4.3%) from the 15,850 counted in the 1990 Census.