WASHINGTON — President Biden will withdraw American combat troops from Afghanistan by Sept. 11, declaring an end to the nation’s longest war and overruling warnings from his military advisers that the departure could prompt a resurgence of the same terrorist threats that sent hundreds of thousands of troops into combat over the past 20 years.

In rejecting the Pentagon’s push to remain until Afghan security forces can assert themselves against the Taliban, Mr. Biden forcibly stamped his views on a policy he has long debated but never controlled. Now, after years of arguing against an extended American military presence in Afghanistan, the president is doing things his way, with the deadline set for the 20th anniversary of the terrorist attacks.

A senior Biden administration official said the president had come to believe that a “conditions-based approach” would mean that American troops would never leave the country. The announcement is expected on Wednesday.

Mr. Biden’s decision would pull all American troops out of Afghanistan 20 years after President George W. Bush ordered an invasion after the Sept. 11 attacks on New York City and the Pentagon, with the goal to punish Osama bin Laden and his Qaeda followers, who were sheltered in Afghanistan by their Taliban hosts.

The war was launched with widespread international support — but it became the same long, bloody, unpopular slog that forced the British to withdraw from Afghanistan in the 19th century and the Soviet Union to retreat in the 20th.

Nearly 2,400 American troops have died in Afghanistan in a conflict that has cost about $2 trillion. Mr. Biden’s Democratic supporters in Congress praised the withdrawal, even as Republicans said it would risk American security.

“The U.S. went into Afghanistan in 2001 to defeat those who attacked the U.S. on 9/11,” Senator Tim Kaine, Democrat of Virginia, said in a statement. “It is now time to bring our troops home, maintain humanitarian and diplomatic support for a partner nation, and refocus American national security on the most pressing challenges we face.”

Jon Soltz, an Iraq war veteran and the chairman of the progressive veterans group VoteVets, said that “words cannot adequately express how huge this is for troops and military families, who have weathered deployment after deployment, with no end in sight, for the better part of two decades.”

But Mr. Biden’s decision drew fire from Republicans.

“This is a reckless and dangerous decision,” said Senator James M. Inhofe of Oklahoma, the ranking Republican on the Senate Armed Services Committee. “Arbitrary deadlines would likely put our troops in danger, jeopardize all the progress we’ve made, and lead to civil war in Afghanistan — and create a breeding ground for international terrorists.”

President Donald J. Trump had set a withdrawal deadline for May 1, but he was known for announcing, and reversing, a number of significant foreign policy decisions, and Pentagon officials continued to press for a delay. Mr. Biden, who has long been skeptical of the Afghan deployment, spent his first three months in office assessing that timeline.

The Afghan central government is unable to halt Taliban advances, and American officials offer a grim assessment of prospects for peace in the country. Still, American intelligence agencies say they do not believe Al Qaeda or other terrorist groups pose an immediate threat to strike the United States from Afghanistan. That assessment has been critical to the Biden administration as it decided to withdraw most of the remaining forces from the country.

A senior administration official said the troop withdrawal would begin before May 1 and conclude before the symbolic date of Sept. 11. Any attacks on withdrawing NATO troops, the official said, would be met with a forceful response.

Taliban leaders have long pledged that any breach of the deadline means that their forces will again begin attacking American and coalition troops. Under a withdrawal deal negotiated during the Trump administration, the Taliban mostly stopped those attacks — but in past weeks, they have rocketed American bases in Afghanistan’s south and east.

In public statements on Tuesday, Taliban leaders focused not on Mr. Biden’s decision for a full withdrawal — leaving behind a weak central government that has proved incapable of halting insurgent advances around the country — but rather on the fact that the administration was going to miss the May 1 deadline.

“We are not agreeing with delay after May 1,” Zabihullah Mujahid, a Taliban spokesman, said on local television. “Any delay after May 1 is not acceptable for us.”

The American-led war in Afghanistan was won, and lost, several times over the past two decades.

The initial campaign — in which relatively small numbers of Special Operations forces partnered with local Afghan militias supported by devastating American air attacks — was quickly successful in forcing Qaeda and Taliban leaders to flee, mostly into Pakistan, by late 2001 and early 2002.

Many military analysts praised the mission — its swift success with a deployment of only limited numbers of ground troops — as a near masterpiece of planning and war-fighting.

The war then evolved, and expanded, from a counterterrorism mission to one devoted to nation-building, democratization and securing rights for women. But the inability to create effective local security forces allowed the Taliban to stage a comeback, prompting a significant surge of foreign troops back into the country starting in 2009, an effort that amounted to a second invasion.

Indeed, areas were cleared of Taliban fighters. But that success, too, proved unsustainable. And in another front in the United States’ post-9/11 wars, the initial victory in Afghanistan may have led the Bush administration to believe that its decision to invade Iraq in early 2003 would also bring similar, swift success.

Biden administration officials said that the United States would reposition American troops in the region to keep an eye on Afghanistan and on the Taliban, and would hold the Taliban to a commitment that there would not be a re-emergence of a terrorist threat on American or Western interests from Afghanistan.

But it was unclear what that meant or how far those repositioned forces would go to protect, for example, the fragile Afghan government or Afghan national security forces.

Biden administration officials said that some troops would remain in the country to protect the American diplomatic presence in Afghanistan — a standard practice.

Mr. Biden’s top aides have said he is keenly aware of the risks of a total security collapse transpiring in Kabul, the Afghan capital, if all Western troops leave, and he has privately described a fall-of-Saigon scenario as haunting.

But in private meetings in recent weeks, the president has also questioned whether the small remaining contingent of Americans can accomplish anything after 20 years during which almost 800,000 U.S. troops have been deployed, or whether it will ever be possible to bring them home. Cost for the war and reconstruction efforts is estimated at about $2 trillion.

Mr. Biden’s own inclination, when he was President Barack Obama’s vice president, was toward a minimal American presence, mainly to conduct counterterrorism missions. But as president, aides said, Mr. Biden must weigh whether following such instincts would run too great a risk of the Taliban overwhelming government forces and taking over Afghanistan’s key cities.

It is unclear how the administration will fulfill its pledge to prevent Al Qaeda from establishing a larger presence in the country — and possibly use it once again as a haven to launch attacks against the United States — if the Taliban do not honor their promise to sever ties with the terrorist organization.

“While not impossible, I think this will make it much harder to remain focused on our counterterrorism objectives,” Gen. Joseph L. Votel, a retired head of the military’s Central and Special Operations Commands, said in an email. Effective counterterrorism “requires good intelligence, good partners, good capabilities and good access,” he added.

“All of these will be challenged,” General Votel said.

The United States maintains a constellation of air bases in the Persian Gulf region, as well as in Jordan, and the Pentagon operates a major regional air headquarters in Qatar. But launching long-range bomber or armed drone missions is risky and time-consuming, and not necessarily as effective in combating hostile targets that pop up suddenly or have time to move out of striking distance.

Instead of declared troops in Afghanistan, the United States will most likely rely on a shadowy combination of clandestine Special Operations forces, Pentagon contractors and covert intelligence operatives to find and attack the most dangerous Qaeda or Islamic State threats, current and former American officials said.

Mr. Biden’s decision on withdrawal was reported earlier Tuesday by The Washington Post.

Military and other officials who favored troops remaining in Afghanistan longer had used a similar classified intelligence assessment to argue for a slower drawdown, worried that an exit of American troops could set off a wider civil war and an eventual return of terrorist groups.

And while the new withdrawal date gives some breathing room to Afghanistan’s beleaguered security forces — who most likely will be propped up by American military support over the summer — the fate of President Ashraf Ghani’s administration remains murky.

Peace negotiations between the Afghan government and the Taliban that began in September in Doha, Qatar, have mostly stalled. In a bid to jump-start the process once more, the Biden administration has pushed for a new round of talks in Turkey — tentatively scheduled for April 24. The idea is for both sides to agree to some sort of framework for a future government and a lasting cease-fire, but experts think that is unlikely as the Taliban believe they can defeat the Afghan militarily.

Over the past year, Afghan security forces have lost territory from repeated Taliban assaults, and have relied on American air power to beat back the insurgents. With the stakes high and the Afghan government’s credibility waning, militias — once the main power holders during the Afghan civil war in the 1990s — have rearmed and reappeared, even challenging Afghan security forces in some areas. Many Afghans have seen their emergence as a troubling sign of what lies ahead for their country.

Afghan officials are afraid that Mr. Biden’s decision to keep American troops in Afghanistan beyond the May 1 deadline, as outlined in last year’s peace deal, would mean pressure on the government in Kabul to release the roughly 7,000 Taliban prisoners the insurgent group has long asked to be freed.

Right now, those remaining prisoners and the lifting of United Nations sanctions were some of the last vestiges of leverage the United States has held over the Taliban. But the Afghan government has been staunchly opposed to any further prisoner release.

Helene Cooper and Eric Schmitt reported from Washington, and Thomas Gibbons-Neff from Kabul, Afghanistan. Reporting was contributed by Julian E. Barnes and Michael Crowley from Washington, and Najim Rahim and Fahim Abed from Kabul.