General Sir Nick Carter, the Chief of the Defence Staff, said it was “not a decision we hoped for” but added that the UK respected the stance taken by the new administration.
His comments come after Mr Biden announced this week that the 2,500 remaining troops would leave Afghanistan by 11 September, the 20th anniversary of the 9/11 attacks on the US.
This marked an extension of the 1 May deadline set by his predecessor, Donald Trump.
Mr Biden said: “It’s time to end America’s longest war. It’s time for American troops to come home.”
Nato allies including the UK confirmed they would also withdraw their armed forces. Britain is to begin pulling out its remaining 750 military trainers from next month.
Gen Carter acknowledged the final withdrawal of international forces after two decades could lead to a return of the warlords but said the situation may not be “quite as bad” as some were predicting.
He told BBC Radio 4’s Today: “It is not a decision that we hoped for but we obviously respect it. It is clearly an acknowledgement of an evolving US strategic posture.”
He said he felt a “great deal of pride” at what the British armed forces had achieved during their time in the country.
“We went into Afghanistan back in 2001 to prevent international terrorism ever emerging from Afghanistan,” he said.
“In the last 20 years there has been no international terrorist attack mounted from Afghanistan. I think that is a great tribute to our armed forces and of course to the armed forces of the Nato countries that have been committed to this.”
Gen Carter said Afghanistan had “evolved hugely” over the past 20 years, while the Taliban had also changed during that time.
The Taliban refers to itself as the Islamic Emirate of Afghanistan. While it stopped attacking international forces as part of national peace talks, it has continued to fight the Afghan government.
The BBC reported that last month, the Taliban threatened to resume attacking foreign troops that remained in the country on 1 May. The group’s “shadow mayor” in the Balkh district, Haji Hekmat, told the broadcaster: “We have won the war and America has lost.”
Some individuals involved in peace talks with the Taliban said Mr Biden’s decision to pull troops out has jeopardised Washington’s efforts and increased the chances of an upsurge in violence.
Ashley Jackson, from the Overseas Development Institute, said: “Biden’s announcement decreases any leverage the international community has left over them, and helps the Taliban justify refusing to attend.”
But Gen Carter believes the Taliban “is not the organisation it once was”.
“It is an organisation that has evolved in the 20 years that we have been there and I think they recognise that they need some political legitimacy,” he said.
“I would not be surprised if a scenario plays out that actually sees it not being quite as bad as perhaps some of the naysayers at the moment are predicting.
“The Afghan armed forces are indeed much better trained than one might imagine. I think they could easily hold together and all of this could work out. We will just have to see.
“At the end of the day, the Afghan people are looking for stability, they are looking for peace, and that is not lost on the Taliban.”
Additional reporting by agencies