Finally a question I can try to make a dent in!
After the surrender at Yorktown in 1781, the British ended up appointing General Sir Guy Carleton to be the new Commander in Chief of the British forces in the Americas. Carleton, remembered more for his later career as a statesman in Canada than for his military leadership, would be given the exhausting task of organizing the evacuation of the British forces from the Colonies. The negotiation, capitulation and evacuation of the British Forces in America was a process that would last in to 1783.
The last major British garrison in the newly minted United States was housed in New York city. Negotiations dragged on while Carleton dealt with the logistics of a large scale evacuation by sea. The Treaty of Paris of 1783 stipulated what the British could take with them, and what they could leave behind. According to the treaty, American property was to be returned, while the lands and properties of loyalists who remained in America was also meant to be respected.
A particular point of contention as the British packed up and left from New York was that thousands of African Slaves had fled across British lines over the course of the war, many of whom had fought for the British or assisted the war effort as non-combatants such as guides. American negotiators led by Washington insisted that these were American property, and must be surrendered in accordance with the Treaty of Paris. Carleton contended that he was obliged to honor the policies of several of his predecessors, such as Lord Dunmore and Sir Henry Clinton, who had promised to emancipate slaves who crossed into British lines.
The final evacuation was carried out in November 1783. By that time, Carleton had issued out certificates of emancipation and evacuated approximately Three-Thousand slaves out of New York, into Nova Scotia. Several issues rankled in the wake of the evacuation, including the British removal of Slaves, and the Americans' seizure of Loyalist property. Additionally, several British forts remained garrisoned somewhat outward of the Canadian border. These complaints went unredressed for a whole decade, and remained points of argument through the negotiations for the Jay Treaty in 1794, which attempted to normalize foreign relations between Britain and the United States.
Primary Sources
British Headquarters (Sir Guy Carleton) Papers, 1747-1783, Public Record Office, London.
Dallas, Alexander James. Features Of Mr. Jay’s Treaty. To Which is Annexed, A View Of The Commerce Of The United States, As It Stands At Present, And As It Is Fixed By Mr. Jay’s Treaty. Philadelphia: 1795
The Revolutionary Diplomatic Correspondence of the United States, edited by Francis Wharton, 377. Vol. 6. Washington: U.S. Govt. Print. Off., 1889.
Secondary Sources
Jasanoff, Maya. Libertys Exiles: American Loyalists In The Revolutionary World. New York: Vintage Books, 2012.
O’Shaughnessy, Andrew Jackson. The Men Who Lost America: British Command During The Revolutionary War and the Preservation of the Empire. London: Oneworld, 2014.
Schama, Simon. Rough Crossings: Britain, The Slaves, And The American Revolution. New York: Harper Perennial, 2007.
Weren't there still a considerable amount of British soldiers still hanging around though? I'm only asking in regard to Jays treaty which I'm pretty sure was well after 1783