Thomas Edmund Molloy was born in Nashua, New Hampshire on September 4th, 1885. He attended Saint Anselm College in Goffstown, New Hampshire. His Irish parents previously lived in Brooklyn, NY. In 1904, Molloy attended St. Francis College in Brooklyn. After attending school, he decided to study for the priesthood at St. John’s Seminary, in Brooklyn. He also attended North American College in Rome, to further his studies. 

On September 19th, 1908, he was ordained as a priest in Rome. He also earned a doctorate in theology before returning to Brooklyn. When Molloy returned, he was assigned as a curate at St. John’s Chapel. Molloy held many positions in the Brooklyn diocese and rose up the ranks. He was a secretary to Cardinal George Mundelein , then Auxiliary Bishop of Brooklyn and was also his secretary for a short period when the prelate moved to Chicago. After he returned to Brooklyn, he joined St. Joseph's College for Women as the spiritual director and professor of philosophy. He later became president of the institution. 

Molloy was named Auxiliary Bishop of Brooklyn on July 28th, 1920. He was consecrated on October 3rd, 1920. The next year, he was named Bishop of Brooklyn following the death of Bishop Charles E. McDonnell. He was installed on February 15th, 1922. At the time, Molloy became the third Bishop of Brooklyn. 

In 1930, Molloy created the Immaculate Conception Seminary, a labor school where working men could learn the Catholic principles that apply to trade unionism. He also ordered the diocesan clergy to learn about industrial issues to better serve their parishioners. 

On April 7th, 1951, Molloy received the personal title of archbishop from Pope Pius XII. 

On November 15th, 1956, Molloy experienced an attack of pneumonia and suffered a stroke. He passed away at his Brooklyn residence on November 30th, 1956.