[1] Broome studied law with William Livingston, but about 1762 abandoned a legal career to join his brother Samuel in a partnership to import British goods.

In 1775, Broome joined the military for the American Revolution when he was appointed lieutenant colonel of the Second New York City Regiment of Militia, which was commanded by John Jay.

[2] In August 1795, during an outbreak of yellow fever, he was the chairman of the city's Health Committee, appointed by Governor George Clinton the previous year, and kept on by Clinton's rival John Jay despite Broome's prominence at a partisan rally to oppose the treaty Jay had just negotiated with the British since health was not considered a partisan issue.

Broome was elected Lieutenant Governor of New York three times, serving from July 1804 until he died in office in August 1810.

Through his daughter Julia, he was the grandfather of Adele Caroline Livingston (1810/3–1841), who married New York merchant Joseph Sampson (1793–1872),[3] themselves the parents of Adele Livingston Sampson (wife of Frederic W. Stevens and Maurice de Talleyrand-Périgord) and grandparents of Adele Livingston "Daisy" Stevens (1864–1939), who was married to Frederick Hobbes Allen (1858–1937),[5] a prominent international lawyer who was the son of Elisha Hunt Allen (1804–1883), former U.S. Representative from Maine and the United States Minister to the Kingdom of Hawaii from 1856 until he died in 1883,[6] and the grandson of Samuel Clesson Allen (1772–1842), a Senator from Massachusetts.