Question

During the final years of World War II, how did the Allies gain control of the North Atlantic?

Answer 1

I suppose you mean with regard to the submarine threat. The first answer could be: by the use of the "Convoy" technique.

Explanation:

The convoy is a structure that, as in a flock of sheep, concentrates together all the slow and defenseless cargo ships (the sheep) and surrounds them with fast and armed patrol ships (the dogs) to defend them and fight submarines (the wolves).
The idea is very good because isolate ships are easy prey of submarines (also because there aren't enough patrol ships to defend them all!).
In a group it may be easier to strike, torpedoing in the middle and score hits, but the real problem, for a submarine, is now to get near striking range without being sunk.

You have to remember that WWII submarines were slow (few knots submerged for a very limited time going with batteries) and once they were left behind, they would have never had the possibility to catch up with the convoy.

The other thing is that submarines could sink many cargo ships but the Americans were building ships at a rate of one per week, while each German submarine was basically irreplaceable (with the submarine, normally, all the members of the crew were killed; these sailors were very skilled and trained, and, basically, irreplaceable).

On top of this we have to remember some very important (and often overlooked) points of WWII submarine warfare in the Atlantic:

1) Many patrol ships had a device called ASDIC; a precursor of the SONAR that allowed them to detect the presence of a submarine (even if not exactly pinpoint it);

2) The British could "read" encrypted message sent by the German Command to submarines in the Atlantic through intercepts from the INTEL center at Bletchley Park; they could use these information to steer the convoys away from the waiting wolf packs of submarines;

3) Light carriers were introduced to cover the convoys with a constant umbrella of anti-submarine aircrafts.