Mr Clinton, who was in New York to address the General Assembly of the United Nations, was followed at the CTBT signing ceremony by ministers from around the world, including the Foreign Secretary, Malcolm Rifkind, and ministers from France, Russia and China. As many as 65 nations were expected to sign the document at the UN.
Mr Clinton used his speech to the General Assembly to herald the new treaty as the "longest-sought, hardest-fought prize in nuclear disarmament history". But he also urged common action to practise "zero-tolerance" in combating the new dangers facing the world, including international terrorism and the trafficking of drugs, and to pursue reform at the UN.
Even until recently there had been fears that the test ban treaty was in danger of unravelling because of opposition from India, which complains that the treaty fails to set a date for total nuclear disarmament. The treaty was finally opened for signature by a majority vote in the General Assembly on 10 September. Technically, it cannot become international law until all 44 nations known to have some nuclear capability, including India, give the document their signatures.
While suggesting that the signatures delivered yesterday represented a "giant step forward" that will automatically create an "international norm" against further tests, Mr Clinton appealed to India, which has not conducted a test since 1974, to sign the treaty.
Of the treaty, Mr Clinton said: "Some have complained that it does not deliver a mandate for total nuclear disarmament by a date certain. I would say to them, do not forsake the benefits of this achievement by ignoring the tremendous progress that we have made towards that day".
Mr Rifkind echoed Mr Clinton, appealing for everyone to sign the document. "It is the sovereign right of every state to decide whether or not to be bound by international agreements. But it is our firm conviction that this treaty is in the interests of all, and I urge all states to give it their full support".
Gro Harlem Bruntland, the Prime Minister of Norway, told the assembly: "In the annals of history, it will be told that nuclear testing happened over a period of 40 years in the 20th century and then never again."
The fruit of years of often tortuous negotiation, the CTBT should be the definitive offspring of two previous attempts to curb the practice of testing. President Kennedy in 1963 signed the Limited Test Ban Treaty, which outlawed all tests in the atmosphere, in space or underwater. It was followed by the Threshold Test Ban Treaty, which limited the size of explosions that were permitted even underground.
Although the appearance of the US President before the assembly is an annual rite, this year's speech by Mr Clinton speech was unusually poignant. It was delivered against a background of America's continuing failure to pay $1.9bn (pounds 1.22bn) in unpaid dues to the UN and of Washington's avowed intent to block the re-election of Boutros Boutros-Ghali to a second term as Secretary-General.