Details have yet to be released but aides familiar with the negotiations say it includes $1.375bn in funding for 55 miles (88km) of new fencing at the border, a small part of the more than 2,000 miles promised by the president.
The barrier would be built in the Rio Grande Valley, in Texas, using existing designs, such as metal slats, instead of the concrete wall that Mr Trump had demanded.
There was also an agreement to reduce the number of beds in detention centres to 40,250 from the current 49,057, reports say.
The talks had reached an impasse earlier with Republicans strongly rejecting Democrats’ demands for a limit to the number of undocumented migrants already in the US who could be detained by immigration authorities.
The deal was struck in a closed-door meeting in Washington on Monday evening after several hours of talks.
“We got an agreement on all of it,” Republican Senator Richard Shelby said.
“Our staffs are going to be working feverishly to put all the particulars together. We believe that if this becomes law, it’ll keep open the government.”
But, by Monday night, some of the president’s conservative allies had already denounced the deal, with Fox News commentator Sean Hannity calling it a “garbage compromise”.
What did Trump say?
In a crowded stadium with banners saying “Finish the Wall” in El Paso, in Texas, Mr Trump told supporters: “Walls work… Walls save lives.”
He repeated that a border fence in the city, opposite Ciudad Juárez in Mexico, “made a big difference”, even though critics reject his claim as exaggerated and based on misleading data.
“We need the wall, and it has to be built,” said Mr Trump, who has previously threatened to declare a national emergency and fund the wall without Congress.
The idea, however, is disliked even by some fellow Republicans, and Democrats are likely to challenge it in the courts.
The president has backed away from calls to make Mexico pay for a concrete wall, a point he repeatedly made during his presidential campaign, and has already acknowledged that the barrier to be built may not be made of concrete.
As the president spoke, Beto O’Rourke, a former Democratic congressman and potential presidential candidate in 2020, held a counter-rally, accusing Mr Trump of stoking false fear about immigrants with “lies”.
Why is there the risk of another shutdown?
On 25 January, President Trump agreed to a three-week spending deal to end the shutdown and allow Congress to reach an agreement.
The shutdown was triggered by the Democrats’ refusal to approve funds for his promised wall on the border with Mexico.
During the last shutdown, hundreds of thousands of workers were furloughed (put on unpaid leave) in December and January while others in essential services, such as hospital care, air traffic control and law enforcement, worked without pay.