Andrew Elliot was born and educated in Scotland. In 1746 he left Scotland and headed for Philadelphia with an advance of £700. Soon after his arrival in Philadelphia he established himself in trade and gained a reputation as an honest and agreeable man. In 1754 he married Eleanor, the daughter of George McCall and sister of Samuel McCall. Elliot engaged in Philadelphia’s social life on a grand scale, earning seats on the Dancing Assembly and the City Council as well as on the Board of Trustees of the College of Philadelphia (now the University of Pennsylvania).
In 1763, while visiting Scotland, Elliot was appointed Collector of the Port of New York, and then Receiver General of New York. As a result, when Elliot returned to America he moved from Philadelphia to New York, ending his service as trustee of the College of Philadelphia.
When the war broke out with Britain, Elliot remained loyal to the crown, and under the British occupation of New York he served the monarch. First he was made head of the military court of police, then collector of customs, and finally lieutenant-governor of New York. As the war wound down in 1783, and it was clear that the Americans had won, Elliot was made part of a British delegation that met with General Washington and other American envoys. At that meeting he was treated well by the Americans, and he was assured that neither his life or his property were at risk. Despite these assurances, Elliot felt he would not be safe in America and later in the year moved himself and his family to Scotland.
In 1790 he declined a proposal to serve as British Minister to America. He died at his home in Scotland in 1797.