“Our military mission in Afghanistan will conclude on August 31,” he said.
The original timeline predicted US operations would be wrapped up by mid-September, but a Pentagon report announced this week said more than 90 percent of the withdrawal is already complete.
Under advice from top defence officials, Mr Biden is moving to remove the remaining troops as quickly as possible.
“In this context, speed is safety,” Mr Biden said.
Defending his decision, the US president added that US objectives in the country had already been completed.
“We went for two reasons,” he said.
“One, to bring Osama bin Laden to the gates of hell, as I said at the time.
“The second reason was to eliminate Al Qaida’s capacity to deal with more attacks on the United States from that territory.
“We accomplished both of those objectives. Period.”
Mr Biden’s speech comes as Taliban forces continue to gain ground across the country.
However, he denied any notion that a Taliban takeover is “inevitable” in the wake of the US withdrawal.
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Mr Biden also offered assurances to protect Afghan interpreters and other key workers who aided US troops during the conflict.
The president said his administration was already working on arranging flights and special visas.
“There is a home for you in the United States if you so choose,” said Mr Biden.
“We will stand with you just as you stood with us.”
Critics of the withdrawal have made comparisons to the Vietnam War, suggesting the US military is leaving a job half done in Afghanistan just as they did in Vietnam.
However, Mr Biden rejected the comparisons, insisting the troop withdrawal does not mark a “mission accomplished” moment for the US.
He concluded: “No, there’s no mission accomplished.
“The mission was accomplished in that we got Osama bin Laden, and terrorism is not emanating from that part of the world.”