The US has similar agreements with other major economic powers, including China.
After the signing ceremony, Burns said: "The US and Russia were once nuclear rivals. Today, we are nuclear partners with unique capabilities and unique responsibilities for global nuclear leadership."
The access to Russian nuclear technology will be important for the US, where civilian nuclear development has been virtually dormant in the wake of a 1979 reactor accident at Three Mile Island and the 1986 Chernobyl nuclear explosion in the Soviet Union.
The US is especially interested in developments in areas including fast-neutron reactors and recycling nuclear fuel.
The deal could also help Russia in its efforts to establish an international nuclear fuel storage facility by importing and storing spent fuel.
It cannot achieve that goal without signing the deal, since the US controls the vast majority of the world's nuclear fuel.
The fuel storage plans have caused outrage among environmentalists and many ordinary Russians, who fear that such a project would turn the country into the world's nuclear dumping ground.
However, Kiriyenko insisted that the deal did not mean Russia would be importing nuclear fuel.
He said: "Russia is not importing and will not import nuclear fuel."
Work on the nuclear agreement got under way after Vladimir Putin, Russia's president, and George Bush, his US counterpart, pledged to increase cooperation in the nuclear field at the Group of 8 summit in St Petersburg in 2006.
Some analysts believe the US administration's willingness to reverse course and work with Russia appears to reflect Washington's view that Moscow is now a partner in the effort to persuade Tehran to abandon its nuclear programme, rather than a hindrance to it.
Rose Gottemoeller, director of the Carnegie Moscow Centre, a US-funded organisation specialising in the study of Russian domestic and foreign policy, said: "The Bush administration is giving a green light on nuclear cooperation with Moscow.
"This is a nod to the long and friendly relations between the Bush and the Putin administration and it sets the stage for some successful nuclear cooperation with the new administrations in the Kremlin and the White House."
The deal came a day before Dmitry Medvedev succeeds Putin as president.