Mr Trump said that, since 1976, a total of 56 national emergencies have been declared but Congress has not vetoed any of them.
Congress can veto Mr Trump's veto, but it does not look likely that they will have the necessary votes to do so.
Twelve of Trump's fellow Republicans joined Democrats to pass the measure to end the emergency declaration.
Trump rejected entreaties from several Senate Republicans to agree to a compromise that would curtail his national emergency powers and instead framed the vote not as a matter of constitutional concerns, but rather as a litmus test on border security.
"It is definitely a national emergency; rarely have we had such a national emergency", he insisted.
Trump was flanked by border officials and people whose family members were killed by someone who was in the United States illegally. "To defend the safety and security of all Americans, I will be signing and issuing a formal veto of this reckless resolution".
She also says the president "is incredibly disappointed" with Republicans who voted against him.
Lawmakers, including 12 Republicans, had passed the rejection resolution on Thursday in a surprising rebuke of Mr Trump's signature issue.
In challenging Trump on Thursday, only one Republican who is up for re-election next year - Susan Collins of ME - voted for the disapproval resolution.
Many lawmakers said the vote was not necessarily a rejection of the president or the wall, but protections against future presidents - namely a Democrat who might want to declare an emergency on climate change, gun control or any number of other issues. Mike Lee, R-Utah; Rob Portman, R-Ohio; Susan Collins, R-Maine; Lisa Murkowski, R-Alaska; Marco Rubio, R-Fla.; Rand Paul, R-Ky.; Lamar Alexander, R-Tenn.; Roger Wicker, R-Miss.; Roy Blunt, R-Mo.; Jerry Moran, R-Kan.; and Pat Toomey, R-Pa.
Trump tweeted about the political advantage he expects those who supported him will receive.
Mozambique braces for 'extremely dangerous' Cyclone Idai
If a cyclone hits further north, it usually draws moisture toward it, leaving much dryer air over South Africa's northern parts. Over the ocean, the winds whipped up waves in excess of 10m, but these should reduce as the storm weakens.
Mark Zuckerberg loses two key Facebook executives
Like many other longtime Facebook executives, Cox is unlikely to ever have to work again if he doesn't want to. Fidji Simo, vice president of video, games, and monetization, will become the new head of the Facebook app.
Are Savings Accounts a Good Idea?
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