“It’s perhaps not what I would have negotiated myself, but it was an agreement made by the United States government and that means something," Mr Biden said.
He said the withdrawal would begin on May 1 and be complete before the September 11 deadline.
The Defence Department had accused the Taliban of failing to live up to its end of the Doha agreement as the violence in Afghanistan continued to intensify.
A UN report released on Wednesday found that civilian casualties in Afghanistan have increased by 29 per cent, with about 1,783 civilians killed or injured in the first three months of 2021.
Mr Biden said he spoke about his decision on Tuesday with former president George W Bush, who launched the war in 2001 after Al Qaeda attacks on the World Trade Centre and the Pentagon.