Those in Afghanistan will be cut from about 5,000 down to 2,500 by mid-January, officials said. In Iraq they will be reduced from 3,000 to 2,500.
President Trump has previously said he wants "all" troops home by Christmas.
He is refusing to concede the 3 November election to Joe Biden.
The withdrawal should be finished by 15 January, US media reported, just days before Mr Biden's inauguration as president.
But Mr Trump's reported plan is facing rare criticism from a fellow Republican - Senate leader Mitch McConnell, who warned militants would "love" the idea.
Speaking on the floor of the upper chamber on Monday, the Kentucky senator said: "We're playing a limited - limited - but important role in defending American national security and American interests against terrorists who would like nothing more than for the most powerful force for good in the world to simply pick up our ball and go home.
"They would love that."
BBC News
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