The Gulf of Mexico doesn't technically "end" and the Atlantic Ocean "begin" in a distinct, defined line. They are connected, with the Gulf of Mexico flowing into the Atlantic Ocean through the Straits of Florida.

Think of it as a large bay, the Gulf of Mexico, connected to a much larger body of water, the Atlantic Ocean.

The Straits of Florida are the narrow passage between the southern tip of Florida and Cuba. This is the primary connection between the Gulf of Mexico and the Atlantic Ocean.

While there's no specific point where one ends and the other begins, the Straits of Florida is the point where the two bodies of water mix and influence each other.