Relations between the two countries have been marked by differences over national interest in recent years.
Arms control will top the agenda of the summit. The Soviet-era Start I accord expires in December.
The two leaders are also expected to discuss regional issues such as Iran, European security and Afghanistan during the two-day visit.
President Obama will hold talks with Vladimir Putin, currently prime minister and formerly president, on Tuesday.
Many analysts say he still in the driving seat in the Russian government.
Both sides have made clear their desire to improve, or "reset", relations between Washington and Moscow.
But BBC diplomatic correspondent Jonathan Marcus, who is in Moscow, says that is not going to be easy given the different perceptions of their national interests the two sides bring to the table.
Under the previous Bush Administration, relations between Washington and Moscow were almost as bad as during the Cold War, so there is ample opportunity for improvement, he adds.
'Difficult situation'
Mr Obama flew out of Andrews Air Force Base aboard Air Force One on Sunday evening, together with his wife and two daughters.
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Hunting out former Cold War bases
He is due to begin his visit by laying a wreath at the Grave of an Unknown Soldier near the Kremlin wall, before talks with Mr Medvedev.
The Russian president said in an interview for Italian media released on Sunday that US missile shield plans for Europe put a "very prominent nuclear country like Russia... in a difficult situation".
The White House co-ordinator for weapons of mass destruction, Gary Samore, ruled out any final agreement on renewing Start being reached this week, but he did see an "announcement" being made.
"I think you will see an announcement that indicates some progress toward reaching that objective," he told reporters.
On Afghanistan, the US is confident of obtaining Moscow's approval for flying troops and weapons through Russian airspace.
President Obama will also meet Russian journalists and civil society activists.
Low-key feel
A University of Maryland opinion poll released on Sunday suggests that 75% of Russians believe the US abuses its greater power and only 2% have "a lot of confidence" that Mr Obama will do the right thing in world affairs.
Neither of Russia's main TV news bulletins on Sunday evening led with the impending US visit.
"This is being played as essentially a low-key visit that shows the American leadership's respect for the Russian leadership," Dmitry Trenin, head of the Moscow Carnegie Centre think-tank, told Reuters news agency.
"This is not some star coming to town."
Nonetheless, correspondents say Mr Obama can expect a smoother reception than he received on a 2005 visit to Russia when he and other visiting US Congressmen were detained for three hours at an airport in the Urals city of Perm.
They were kept in an "uncomfortably stuffy room adjacent to the tarmac", a US spokesman said, as they resisted Russian customs officials' demands to search their plane.
Mr Obama later brushed off the incident in his book The Audacity of Hope, saying "It wasn't the Gulag".
