Obama looks forward to "discussing our continued transition in Afghanistan, and our shared vision of an enduring partnership between the United States and Afghanistan," a White House statement said.
The Afghan leader has expressed support for keeping US troops in Afghanistan but sensitive details -- including immunity for American soldiers and the transfer of detainees into Afghan custody -- are still under negotiation.
Karzai's relationship with Washington has been troubled in recent years and fears remain that attention for Afghanistan, heavily dependent on international aid, could plummet after 2014, plunging it back into political turmoil.
The US Defense Department has reportedly prepared plans to leave roughly 3,000, 6,000 or 9,000 US troops in the war-wracked state.
General John Allen, commander of US and NATO forces in Afghanistan, had earlier suggested leaving 6,000 to 20,000 US troops, US media reports have said.
Outgoing Defense Secretary Leon Panetta has said the force would focus on preventing Al Qaeda, which was sheltered by the 1996-2001 Taliban government, from regaining a firm foothold in Afghanistan.
The number of foreign troops battling the Taliban-led insurgency has already fallen to 100,000 from about 150,000. There are currently 66,000 US troops, down from a maximum of about 100,000.
Obama last visited Kabul in May -- one year after US commandos killed Al-Qaeda chief Osama bin Laden -- when he signed a pact on future relations and declared that the "time of war" was ending in Afghanistan.
The conflict has become increasingly unpopular in the United States, but some lawmakers in Washington have accused Obama of pushing for a hasty exit.
Karzai, who left Kabul on Monday, is expected to kick off his US trip by visiting his wounded spy chief, Asadullah Khalid, at an American hospital on Tuesday.