Twelve Republicans joined Democrats in the Senate to pass the measure, concerned that the president had overstepped his authority.
Trump's veto sends the resolution back to the US House of Representatives, which is expected to pick it up after the week-long congressional recess.
White House spokeswoman Mercedes Schlapp would not say when the veto would happen, but told reporters Friday Trump is "doing what he believes is his constitutional duty, which is to protect the American people".
"People hate the word invasion, but that's what it is". Homeland Defense Secretary Kirstjen Nielsen, Attorney General William Barr and Vice President Mike Pence were among those who praised Trump's veto during the Oval Office ceremony. Angel Moms, mothers of children killed by illegal aliens, were also in attendance.
Congressional critics do not appear to have the votes to override Trump's veto.
According to The Hill, the House will attempt to override the president's veto on March 26, but because a two-thirds majority is necessary to issue such an override, it's unlikely to find success.More news: Reputed Boss Of Gambino Crime Family Gunned Down In New York
More news: Families of Ethiopia plane crash victims storm out of meeting with airline
More news: Pain-free Tiger hopes putter warms up at Players
The vote came a day after the Senate called for an end to United States military support for the Saudi-led war in Yemen, marking the second instance in two days that a Senate that has been mostly deferential to Trump took a position against him.
It is being challenged in court as an unconstitutional usurpation of Congress' power of the purse.
"I think actually a national emergency was designed for a specific objective like this, so we have a great case", Trump said.
The Republican senators who rebuked Trump were unwavering in their justification, saying Thursday they viewed the unilateral move as unconstitutional and creating a risky precedent for future presidents. "To me, border security is national security".
He also noted that despite record numbers of apprehensions at the border, there was not enough space to detain them all. His signature ended a 35-day partial shutdown of the federal government, which had been triggered by a showdown after Congress refused to appropriate the $5.7bn he requested to start construction at the border.
The national emergency I declared last month was authorized by Congress under the 1976 National Emergencies Act, and there haven't been too many that are bigger [emergencies] than we have right at our own border. Trump had campaigned for president promising Mexico would pay for the wall.