The decision, to be announced by Obama in a White House Rose Garden event at 2:45 p.m. EDT (1845 GMT), means that the president will leave office in early 2017 with no measurable troop strength in Afghanistan.
The number emerged after Obama met with U.S. military commanders at Bagram Air Base in Afghanistan on Sunday as the United States winds down the longest war in American history, which began following the Sept. 11, 2001 attacks.
The United States now has about 32,000 troops in Afghanistan, along with NATO allies and others. Most of the U.S. forces will have been withdrawn by the end of 2014.
Under the scenario envisioned by the president, the 9,800 troops would remain behind into next year. By the end of 2015, that number would be reduced by roughly half, the officials said.
By the end of 2016, the U.S. presence would be cut to a normal embassy presence with a security assistance office in Kabul, as has been done in Iraq, the officials added.
Some Republicans greeted the news with skepticism, saying they feared Obama was abandoning Afghanistan. They continued a drumbeat of criticism of the president's handling of foreign policy and national security ahead of a speech on the subject Obama is to give on Wednesday at the U.S. Military Academy in West Point, New York.
"Holding this mission to an arbitrary egg timer doesn't make a lick of sense strategically," said Republican Representative Howard McKeon, who chairs the House of Representatives' Armed Services Committee.
Republican Senator Lindsey Graham said Obama was at risk of "repeating some of the same mistakes he made in Iraq," where sectarian violence escalated after the U.S. pullout.
With Afghans about to elect a new president, the United States is looking past the tenure of current Afghan President Hamid Karzai, who had irked Obama by refusing to sign a bilateral security agreement.
U.S. officials are expressing increasing confidence that the next Afghan president will sign the treaty, which Obama wants before the United States will agree to leave behind troops to help train Afghan forces and conduct operations against al Qaeda.
The two leading candidates in Afghanistan's presidential race, Abdullah Abdullah and Ashraf Ghani, have both pledged to sign the security agreement as soon as possible should they be elected in the second round of voting set for June 14.
Karzai's refusal to sign the agreement has exacerbated concerns about the country's prospects for stability as the Taliban insurgency rages on and has contributed to a steep economic downturn in recent months.