US President Barack Obama and Russian President Dmitry Medvedev have hailed the New Start nuclear arms treaty as a "historic event", the White House says.
In a telephone call on Thursday, Mr Medvedev congratulated Mr Obama on achieving Senate approval of the pact.
Mr Obama in turn said that the two had a "very productive year".
The US Senate approved the pact, which would reduce nuclear arsenals and allow their inspection, on Wednesday after some Republicans agreed to back it.
'Extra Russian checks'
In Russia, meanwhile, the Speaker of the State Duma (lower house), Boris Gryzlov, said MPs might approve the pact on Friday, with the upper house, the Federation Council, approving it in next year.
Mr Gryzlov said the Russian parliament would first check that the US Senate's ratification motion had not changed the text of the agreement.
The US Senate on Wednesday approved the treaty by 71 votes to 26, after months of wrangling and over the objections of some of the top Republicans in the chamber. Thirteen Republican Senators broke with party leadership and voted with the Democrats.
Correspondents say the ratification will be seen as a foreign policy success for Mr Obama.
He has argued that ratification of New Start is vital to US national security and made the agreement a key plank of the president's much-heralded "re-set" of relations with Russia.
After the vote, Secretary of State Hillary Clinton said in a statement: "A responsible partnership between the world's two largest nuclear powers that limits our nuclear arsenals while maintaining strategic stability is imperative to promoting global security."
The New Start treaty, which will replace its lapsed predecessor, Start (Strategic Arms Reduction Treaty), was signed by the two presidents in April 2010.
It trims US and Russian nuclear arsenals to 1,550 deployed nuclear warheads - a cut of about 30% from a limit set eight years ago.
The treaty would also allow each side visually to inspect the other's nuclear capability, with the aim of verifying how many warheads each missile carries.
A previous inspection regime - part of the old Start treaty - expired a year ago.
In addition, there will be legally binding limits on the number of warheads and missiles that can be deployed on land, on submarines, and on bombers, at any one time.