Dwyer was born on March 4, 1957, in Manhattan, one of four sons of Philip and Mary (née Molloy) Dwyer, who were Irish Catholic immigrants. Dwyer graduated from the Msgr. William R. Kelly School in 1971. At the Loyola School, he played several sports, joined the drama club, was editor of the school newspaper and graduated in 1975. He later attended Fordham University where he earned a bachelor’s degree in general science, in 1979. While in Fordham, future Governor of New York Andrew Cuomo was his classmate. In 1980, he received a master’s degree from the Columbia University Graduate School of Journalism.