After all but ignoring the issue for two years, the Biden administration has announced a deal with Mexico under which the tens of thousands of Venezuelan migrants showing up at the southern border will be returned to Mexico.

In exchange, the United States has agreed to double the number of work visas available for low-skilled immigrants and allow thousands of Venezuelans to enter America by air and avoid the perilous overland routes through Central America that many have undertaken in recent months.

The move marks a return to the Trump-era Title 42 restrictions — the “remain in Mexico” policy panned by many Democrats, including President Biden — that blocked all asylum requests at the border in the name of Covid prevention. Mr. Biden has been attempting to lift the policy since he took office, but a federal judge blocked the administration from doing so in May.

“These actions make clear that there is a lawful and orderly way for Venezuelans to enter the United States, and lawful entry is the only way,” the homeland security secretary, Alejandro Mayorkas, said. “Those who attempt to cross the southern border of the United States illegally will be returned to Mexico and will be ineligible for this process in the future. Those who follow the lawful process will have the opportunity to travel safely to the United States and become eligible to work here.”

The Mexican government said the shift is an attempt by the two countries to ensure a smooth migration process. “With this program, those who seek to enter the United States will be able to do so in a more orderly, safe, regular and humane manner. The program discourages undocumented crossings that put migrants’ safety at risk,” it said in a joint statement.

As many as 24,000 Venezuelans will be able to fly to America in a program similar to one offered to refugees displaced by the war in Ukraine. They will need to apply online and be able to stay and work for up to two years if they have a financial sponsor in the United States.

In August alone, more than 25,000 Venezuelans fleeing repression and an economic meltdown in their home country were stopped at the southern border, four times the number who were stopped in August 2021. Almost 7 million Venezuelans have fled their country since the economy collapsed in 2014.

From now on, any Venezuelan apprehended at the border will be returned to Mexico. Additionally, those caught entering Mexico or Panama illegally will be locked out of the new amnesty program. Until now, Mexico has accepted deportees only under Title 42 if they are from Guatemala, Honduras, El Salvador, or Mexico.

Mexico, which described the new policy as temporary, gave no indication of just how many Venezuelans it would allow back into its territory under the deal. The 24,000 slots offered to airborne Venezuelans is less than the number who crossed the border from Mexico in August alone. More than 150,000 were stopped in the fiscal year that ended September 30.

In a related announcement Wednesday, the homeland security department said it would increase the number of H-2B visas available for low-skilled workers in the 2023 fiscal year to nearly 130,000 from 66,000 in 2022. As many as 20,000 of those will be set aside for migrants from Central America and Haiti.

Mr. Majorkas pitched the increase as an attempt by the administration to meet the needs of American businesses, many of which are struggling to recruit and retain workers. “This full year allocation at the very outset of the fiscal year will ensure that businesses can plan for their peak season labor needs,” he said.