Officials said the tough new curbs should start as soon as the order comes into effect at midnight on Wednesday as the number of people crossing without proper documentation is already above the threshold.
Asylum seekers would again be allowed to enter once the daily numbers dropped to 1,500.
“This action will help us gain control of the border,” said Biden, who was flanked by elected officials from border states.
Biden slammed Trump and Republicans for what he called the “extremely cynical, political move” of failing to cooperate with him and blocking billions of dollars in funding for the border.
“Let’s fix the problem and stop fighting about it,” he said.
The move is the toughest ever by a Democratic president and sees Biden moving closer to Republican Trump’s own signature border policies, amid polls showing the issue heavily dragging on Biden’s re-election chances in November.
Trump blasted his rival’s move, saying Biden “surrendered” the border to illegal immigration.
“Millions of people have poured into our country – and now, after nearly four years of his failed, weak leadership, pathetic leadership, crooked Joe Biden is pretending to finally do something about the border,” Trump, 77, said in a video posted to his Truth Social media platform.
He added the border restrictions were all for “show” ahead of their presidential debate later this month.
Republican House Speaker Mike Johnson, a Trump ally, quickly labelled the move as “window dressing”.
Trump’s campaign meanwhile repeated his frequent claims that illegal migrants are responsible for surges in violent crime – an allegation not supported by any major police or academic data.
Migrants entering the United States are normally allowed to claim asylum if they face harm or persecution on the grounds of race, religion, nationality, political opinion, or membership in a particular social group.
But many spend years waiting for their claims to be processed, with critics saying that people often cross purely for economic reasons and then game the system to remain in the United States.
Under Biden, border crossings have surged to record levels, rising to a monthly peak of around 300,000 – 10,000 a day – in December.
Most are from Central America and Venezuela as they flee poverty, violence and disasters exacerbated by climate change, but growing numbers are also coming from other parts of the world to Latin America before making the treacherous trip north to the United States.
The numbers have fallen considerably in recent months, to some 179,000 in April, but polls show it is still one of Biden’s biggest electoral liabilities.
Biden’s plan will anger leftist Democrats and will almost certainly be challenged in court by civil rights groups.
A senior White House official moved to defuse criticisms that Biden is effectively copying Trump, saying that while in office, the Republican “demonised immigrants, instituted mass raids, separated families at the border and put kids in cages. Their policies went against our values as a nation.”
Trump spent his time in office trying to build a wall on the Mexican border and has drastically ramped up his anti-immigration rhetoric as he seeks a White House comeback.