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The agreement means the United States will sell Polaris missiles to the UK.
The President has made a similar offer to France in the hope of establishing a tripartite nuclear deterrent against the countries of the Eastern Bloc.
Polaris, a two-stage solid-fuelled rocket system, is designed to be fired underwater from a submarine. It carries a half-megaton nuclear warhead at a speed of 17,500 mph (28,160 kph).
The British Government would construct the submarines and develop warheads for Polaris with technical support from the US.
The deal has been described in the US press as a landmark in military and political development in the Western world.
It is also regarded as the most constructive meeting held between President Kennedy and Mr Macmillan.
However, there are now fears Britain will be too reliant on the US for its nuclear deterrent in spite of the fact that the nuclear element of the weapons system will be supplied by Britain.
At the end of the three-day summit, the two leaders issued a joint statement.
In it, Mr Macmillan made it clear that Polaris missiles would be used for international defence of Nato countries, except where Britain's "supreme national interests are at stake".
This phrase is designed to show the British nuclear force is politically independent of the US.
Cuban missile crisis
President Kennedy also sent a letter to France's President Charles de Gaulle offering to sell Polaris as well as provide technical support.
It is hoped this will not only heal the current rift between France and Britain over Mr Macmillan's "special relationship" with the US and Britain's wish to enter the EEC, but also strengthen Nato as a whole and allow France a greater role within it.
If France rejects the agreement, it will still be valid between Britain and America.
The talks come just two months after the Cuban missile crisis when it was revealed the Soviet Union's leader, Nikita Khrushchev, had set up nuclear missile bases on America's doorstep.
In this context, President Kennedy and Mr Macmillan emphasised the need for a unified defence programme.
"In strategic terms, this defence is indivisible and it is their conviction," said the statement, "that in all ordinary circumstances of crisis or danger it is this very unity which is the best protection of the west."
The controversial American Skybolt missile project will be abandoned due its high cost and questions about how long it would have taken to complete.
The first of a dozen Polaris submarines are due to go into service in the UK within five years. Each submarine will cost around £35m each and each missile costs £350,000. The total cost of the nuclear naval deterrent is estimated at about £300m.
The US currently has five Polaris A-1 submarines in service with a range of 1,200 miles (1,931 km).
The A-2 version is being tested from improved Polaris submarines and can reach 1,500 miles (2,414km).
A-3 missiles are due to be ready for use in 1964 and have a range of 2,500 miles (4,023km).
Compared with Skybolt missiles which carry warheads of nearly two megatons, Polaris rockets are less powerful.
But they are also less vulnerable because Skybolts are dropped from aircraft while Polaris submarines are much harder to locate.
France eventually declined America's offer of Polaris and the multilateral Nato nuclear agreement was signed without France in January 1963.
In his desire for independence from the Superpowers and a major role on the world stage, De Gaulle ensured that France developed its own nuclear arsenal.
It also withdrew its military bodies from Nato command in 1966 but remained in the alliance's political councils.
HMS Resolution, the first of Britain's Polaris armed submarines, began operational patrols in 1968 and took over from RAF bombers as Britain's strategic nuclear deterrent.
Polaris was replaced by the Trident system during the 1990s.
The Nassau agreement cemented the Anglo-American "special relationship" that had developed during the Second World War.
But the deal confirmed De Gaulle's belief that Britain was a Trojan horse which would allow America a voice in Europe.
For this reason he vetoed Britain's application for membership of the European Economic Community in 1963 and again in 1967.
The Cold War ended after the break up of the Eastern Bloc in 1989. The Czech Republic, Hungary and Poland became the first former Warsaw Pact countries to gain Nato membership in 1999.
In 2004 they were followed by former Soviet republics Estonia, Latvia and Lithuania and Slovenia, Slovakia, Bulgaria and Romania.
Nato members in 1962
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