"The processes that are now taking place in Ukraine are irreversible," he said in an appearance at the Center for Strategic and International Studies.
Ukraine's decision to give up its nuclear weapons earned the country a bundle of U.S. aid and afforded Kuchma an elegant evening at the White House.
"Mr. President, people around the world admire you for your wisdom in leading your country to a non-nuclear future," President Bill Clinton said in remarks at a state dinner for Kuchma on Tuesday night.
"And we applaud your courage in embarking on the difficult task of economic reform," said Clinton.
After a day of meetings Tuesday, the two presidents signed agreements laying out areas for future cooperation and focusing on joint space ventures. Officials signed two other agreements to encourage private investment in Ukraine.
At a news conference after the signings, Kuchma said they had "opened the way to full-fledged cooperation."
Once seen as the problem child of the countries that emerged from the breakup of the Soviet Union, Ukraine moved into favor when it agreed last week to give up its inherited nuclear arsenal, missiles and bombs that made it the world's third-largest nuclear power.
It was a move with immediate consequences for the former Soviet republic.
"It will permit us to strengthen our military relations with Ukraine, it will open up Ukraine to a new range of business and technological opportunities," Clinton told the news conference. "In addition, we pledge to help defray some of the costs for participation by Ukraine in the Partnership for Peace."
Clinton promised $200 million in new U.S. aid over the next two years. Congress already has approved $700 million, half of which was to help dismantle nuclear missiles.
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