Russia had long objected to plans pursued by the administration of former-President George W Bush to base a missile interceptor system close to its borders, calling it a threat to its security.
Kevin Connolly, BBC News, Washington
It would be hard to invent a news story that tied together more strategic and political issues than the Obama administration's decision to change its stance on the deployment of a missile defence shield in Eastern Europe.
It touches on Washington's assessment of Iran's military capabilities. There is an underlying assumption that Tehran's capacity for mounting warheads on long-range missiles does not pose an immediate strategic headache.
It also sends a signal to the peoples of Central Europe about how President Barack Obama proposes to manage the post Cold War order in their neck of the woods in the next few years. And it raises questions about the administration's much-talked-about desire to "hit the reset" button on its relationship with Russia.
Mr Medvedev said he would discuss the issues with Mr Obama during a visit to the United Nations in New York next week.
The US move was also welcomed by German Chancellor Angela Merkel.
"I see the decision today as a very hopeful signal that we can overcome the difficulties with Russia and develop a united front to counter the threat of Iran," she said.
However, Republicans in the US have condemned Mr Obama's move.
Senate Minority Leader Mitch McConnell said it was "short-sighted and harmful to our long-term security interests".
Defeated presidential candidate John McCain called the decision "seriously misguided".
"Given the serious and growing threats posed by Iran's missile and nuclear programmes, now is the time when we should look to strengthen our defences, and those of our allies."
Barack Obama: "I'm confident... we have strengthened America's national security"
But Democratic House Speaker Nancy Pelosi said the decision was "brilliant" and clearly based on an accurate summary of the current threats.
The missile shield in question was first confirmed in August 2008, when the US signed a deal with Poland to site 10 interceptors at a base near the Baltic Sea, and with the Czech Republic to build a radar station on its territory.
On Thursday Mr Obama said the review he had ordered had shown the threat from Iran had altered.
There was now a need for a more flexible approach to provide "a stronger, smarter and swifter defence" of US and allied forces in Europe.
Defence Secretary Robert Gates said the first phase of the new strategy would be to deploy "current and proven missile defence systems in the next two years", including the sea-based Aegis and SM-3 interceptors.
BBC defence and security correspondent Nick Childs says the new US strategy is based on mobility and flexibility.
Proven defence systems will be based first on warships and then on land, and will be upgraded over the next decade, he says.
Mr Gates stressed the US was not abandoning missile defence of Europe.
He said negotiations were under way with both Poland and the Czech Republic about deploying upgraded SM-3 interceptors from 2015.
Under the system proposed by former president Bush, ground-based defence missiles would have been sited in Poland and a radar system to detect enemy missiles installed at Brdy in the Czech Republic. Iran's Shahab-3 missile is thought to have a maximum range of 2,000km.
President Barack Obama has shelved plans to site interceptor missiles in Poland. Instead the Aegis and Standard Missile-3 systems will be deployed on US warships based in the Mediterranean, with mobile land-based variants to follow by 2015.
Intercontinental missile ranges
The US has developed missile defence sites in California and Alaska as a deterrent to North Korea, which has unsuccessfully tested a 10,000 km range missile the Taepodong-2. Of the US's strategic rivals, Russia has the longest range missile, the SS-18.
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