Obama plans to deliver a televised address to Americans later on Tuesday.
The US-Afghan Strategic Partnership Agreement will set conditions for a US presence there after a 2014 deadline for the withdrawal of most NATO combat forces.
As he fights for his re-election, Obama is seeking to portray his foreign policy record as a success.
His re-election campaign has made bin Laden's death a key part of that argument, and the president's visit to the country where militants hatched the September 11, 2001 attacks will reinforce that message. It also opens him up to criticism from Republicans, who say Obama has politicised bin Laden's death.
After leaving Washington under cover of darkness late on Monday and flying overnight, Obama arrived at Bagram Air Base before visiting Kabul.
He planned to meet with Afghan President Hamid Karzai at his palace and will later make remarks to troops at Bagram. From Bagram, he also plans to deliver formal remarks about the Afghanistan war at 7:30 pm EDT (2330 GMT).
Obama's speech will focus on the strategic partnership agreement and is likely to put an emphasis on his plans to wind down the costly and unpopular Afghanistan war where nearly 3,000 US and NATO soldiers have died since the country was invaded in 2001.
After a US troop increase that Obama ordered in late 2009, US and NATO forces have managed to weaken Taliban militants, but the movement is far from defeated.
The White House wants to paint Obama's strategy in Afghanistan as successful, despite continued violence there and problems with corruption that have raised concerns about the country's future stability.
Republican Mitt Romney, Obama's likely opponent in the November election, has criticized Obama's handling of Afghanistan, saying the timeline for a withdrawal will only embolden militants and could leave the country vulnerable to a return to power of the Taliban, which ruled Afghanistan prior to the US-led invasion.
Obama plans to host NATO leaders in Chicago on May 20-21 for a summit to discuss the specifics of the troop withdrawals and look at ways to ensure that Afghanistan does not collapse into civil war when foreign forces leave.
(Copyright Thomson Reuters 2012)