The Revolutionary War started in April 1775 when British troops quartered in Boston attempted to seize munitions stored by colonial militias at Concord, Massachusetts.
During the final days of 1776, General George Washington crossed the Delaware River into New Jersey and rolled up outlying British garrisons at Trenton and Princeton. This established a pattern that held for the rest of the war. While at this point the British controlled the territory they occupied with major forces, primarily New York City and Philadelphia, The colonists controlled the rest of the land.
On February 6, 1778, the United States and France signed the Treaty of Alliance and the Treaty of Amity and Commerce. The signing of these treaties signaled official recognition of the new republic. On July 10, 1778, Louis XVI of France declared war against the Kingdom of Great Britain on behalf of the Americans.
The British House of Commons voted to end the war in April 1782. The government of war proponent Lord North was ousted. The British pulled their remaining troops from Charleston, South Carolina, and Georgia in the summer of 1782. On November 30, 1782, preliminary peace articles were signed in Paris and on February 4, 1783, Great Britain formally declared that it would cease combat in North America.
The formal end of the war took place when the Treaty of Paris was signed on September 3, 1783. The Congress of the United States ratified the treaty on January 14, 1784. The last of the British troops in America left New York City on November 25, 1783.