Broom was born on October 17, 1752 at Wilmington, Delaware. His father, James Broom, was a blacksmith and farmer. Broom was homeschooled; as he grew older, he studied surveying—a skill that would eventually allow him to prepare maps for General George Washington prior to the Battle of Brandywine. He eventually turned his hand to a variety of mercantile trades, including shipping and imports. In 1776, Broom became the assistant burgess of Wilmington.
Broom was appointed a member of the Constitutional Convention in 1787, and never missed a session. Though he spoke very little at the convention, he may have helped keep the members in session until their work was completed. Other members of the Delaware delegation to the Convention were Gunning Bedford, Jr., Richard Bassett, John Dickinson, and George Read.
- Was appointed to the Annapolis Convention, but did not attend.
- Father of Congressman James Broom and grandfather of Congressman Jacob Broom.