The Taliban has threatened to resume attacks against U.S. and partner forces if the deadline was not met.
USA officials provided details on Mr Biden's decision on condition of anonymity, speaking ahead of the announcement.
A us intelligence report released at the end of March said that should the USA withdraw, it is likely the Taliban could take over Afghanistan within two to three years and potentially bring al Qaeda back to power in the country.
"The Islamic Emirate responded firmly to Biden's comments and announced that if the occupying forces do not leave by the agreed-upon date, then attacks shall resume", the Taliban warns, repeating an earlier threat to attack American and North Atlantic Treaty Organisation forces should they fail to depart by May 1. "We will leave", Biden said last month.
The Democratic president will publicly announce his decision on Wednesday, the White House said. The U.S., via Secretary of State Antony Blinken, had proposed a peace plan that included an interim government - a plan that Afghan President Ashraf Ghani has resisted, backing elections instead.
Biden's decision suggests he has concluded that the United States military presence will no longer be decisive in achieving a lasting peace in Afghanistan, a core Pentagon assumption that has long underpinned American troop deployments there.
While al-Qaida is not now believed to pose an external threat to the USA, the official said, the country will reposition its counterterrorism assets in the region to monitor and disrupt any potential threats to the homeland.
The Biden official said the withdrawal would begin in May and that the delay was largely logistic, with troops possibly out of Afghanistan well before 11 September.
"We are not staying for a long time".
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Turkey announced on Tuesday that a keenly awaited worldwide conference on the Afghan peace process will be held in Istanbul from April 24 to May 4.
The US national intelligence report states that the Taliban "is confident it can achieve military victory". That was when hijackers crashed passenger jets into the World Trade Center in New York City, the U.S. Defense Department outside of Washington and a field near Shanksville, Pennsylvania.
"We are committed to ensuring that the gains that have been made are not lost, and that is especially true for women in Afghanistan", he said.
The official said other troops serving in Afghanistan from allied countries will also withdraw.
Although successive USA presidents sought to extricate themselves from Afghanistan, those hopes were confounded by concerns about Afghan security forces, endemic corruption in Afghanistan and the resiliency of a Taliban insurgency that enjoyed safe haven across the border in Pakistan.
"That withdrawal may be completed well in advance of September 11", the official said.
About 2 400 USA service members have been killed in the course of the Afghan conflict and many thousands more wounded. Negotiations between Afghanistan's government and the Taliban continue.
The Taliban have promised women could attend school, work and participate in politics but stressed that would be allowed in keeping with Islamic principles - without saying what that might mean.
The reports of the Biden decision come on the same day that a US intelligence report predicted a hard path for Afghan peace talks.
"There is no easy answer", Reed said.