Final answer:
It took about two years to negotiate peace with the signing of the Treaty of Paris in 1783 after the American victory at Yorktown, which marked the beginning of British evacuation from the colonies.
Step-by-step explanation:
After five and a half years of fighting during the American Revolution, it took approximately two years to negotiate peace and evacuate the British from its former colonies. The Parliament of Great Britain voted to end military operations and begin peace negotiations after the American victory at Yorktown.
Finally, the diplomatic negotiations known as the Peace of Paris culminated with the signing of the Treaty of Paris in 1783, which officially ended the conflicts and began the process of evacuation.