President Donald Trump has long called for troops to come home and has criticised US interventions abroad.
The head of Nato warned of a "very high price". Senate Majority Leader Mitch McConnell called the plan "a mistake".
Mr McConnell - usually a staunch defender of Mr Trump - also warned the president against making "any earth-shaking changes in regards to defence and foreign policy" before leaving the White House.
Mr Trump is yet to concede to Democrat Joe Biden, and the cuts are scheduled to take place five days before Mr Biden takes office on 20 January 2021.
The president-elect has said he is "rightly weary of our longest war" in Afghanistan but also said there was a need to "end the war responsibly, in a manner that ensures we both guard against threats to our homeland and never have to go back."
The Biden transition team has not yet commented on the announcement.
In Iraq, the number of US troops will be cut by 500 to 2,500, while the number of service personnel in Afghanistan will fall from 4,500 to about 2,500.
Pentagon says consultations were made Acting US Defense Secretary Chris Miller - who was installed last week after Mr Trump abruptly fired Mark Esper - said the move reflected the president's policy "to bring the wars in Afghanistan and Iraq to a successful and responsible conclusion and to bring our brave service members home".
"We will protect our children from the heavy burden and toll of perpetual war, and we will honour the sacrifices made in the services of peace and stability in Afghanistan, Iraq and around the world," he said.
He did not confirm if the drawdown plan had been endorsed by Gen Mark Milley, chairman of the Joint Chiefs of Staff, but said the decision followed "continuous engagement with the president's national security cabinet".
Mr Miller said the US had met its goal of defeating extremists and helping "local partners and allies to take the lead in the fight". US officials said the withdrawal plans had yet to be hammered out in detail and it was not yet clear which troops would be pulled out, Reuters news agency reports.
Shortly after the announcement, several rockets were fired into the Green Zone in Baghdad and landed near the US embassy. It is the first such attack since Iraqi militias linked to Iran agreed to stop targeting the embassy compound last month. The Iraqi military said an Iraqi child was killed and five civilians were wounded.
US forces have been in Afghanistan since 2001. A US-led coalition ousted the Taliban weeks after the 11 September 2001 attacks in the US by al-Qaeda, which was then based in Afghanistan
The Taliban regrouped and became an insurgent force that by 2018 was active in more than two-thirds of the country The US started withdrawing troops from Afghanistan as part of an agreement signed by the US and the militants in February this year. But violence in the country has increased recently as the group steps up its offensives amid stalled negotiations with the Afghan government
Thousands of US forces are in Iraq as part of an international coalition to fight against the Islamic State (IS) group
Along with Mr McConnell, several other senior Republicans also voiced concerns. Texas Republican congressman Mac Thornberry called the move a "mistake", saying cutting troop numbers would "undercut negotiations" currently under way aiming to bring an end to fighting in Afghanistan.
And Senator Ben Sasse, who sits on the Senate Intelligence Committee, said it was a "weak retreat" and that it was "not grounded in reality and will make the world a more dangerous place."
Nato Secretary-General Jen Stoltenberg, in a rare public show of concern, said "the price for leaving too soon or in an uncoordinated way could be very high". In a statement, he added that Afghanistan risked once again becoming a platform for international militants to organise attacks.
The 30-nation alliance relies heavily on the US forces for logistical support in Afghanistan.
"The US is only going to be able to focus on counter-terrorism operation - it's really going to have to cut back its train, advise and assist mission which means the Afghan government is going to feel the brunt of this," said Seth Jones, senior adviser at the Centre for Strategic and International Studies.