Born in Brooklyn, Cullen attended the local parochial schools, and graduated from St. Francis College in 1880.

Cullen was a member of the New York State Assembly (Kings Co., 3rd D.) in 1896, 1897 and 1898.

He was a delegate to the 1912, 1916, 1920, 1924, 1928 and 1932 Democratic National Conventions; and a member of the New York State Commission for the Panama–Pacific International Exposition in 1915.

Cullen elected as a Democrat to the Sixty-sixth and to the twelve succeeding Congresses and held office from March 4, 1919, until his death in Washington, D.C., in 1944; interment was in Holy Cross Cemetery, Brooklyn.

During his tenure, Cullen was considered a leader of the "Tammany Hall" delegation from New York and served on the powerful House Ways and Means Committee.