Yes. Great Britain formally recognized the United States as a free, sovereign, and independent nation in Article I of the Treaty of Paris, signed September 3, 1783.
The treaty ended the American Revolutionary War. Key terms: Britain acknowledged U.S. independence; established borders (Atlantic to Mississippi, Great Lakes to Florida); granted fishing rights off Newfoundland; addressed Loyalist property and debt repayment; and withdrew British troops. Ratified by the U.S. Congress on January 14, 1784.