Lower courts had deemed
the ban unconstitutional, but the US top court reversed the decision in a
5-4 conservative majority ruling.
At a White House meeting to discuss Mr Trump's proposed border wall he lauded the decision as "a tremendous success".
The court's reversal is viewed as a victory for the Trump administration.
The ban prohibits most people from Iran, Libya, Somalia, Syria and Yemen from entering the US.
Mr Trump said the Supreme Court decision was a "great victory" for the nation and constitution.
"We
have to be tough and we have to be safe and we have to be secure," the
Republican president said in Tuesday's meeting with lawmakers.
"The
ruling shows that all the attacks from the media and the Democrat
politicians were wrong, and they turned out to be very wrong," he added.
He
added: "If you look at the European Union, they're meeting right now to
toughen up their immigration policies because they've been over-run,
they've been over-run.
"And frankly, a lot of those countries are not the same places anymore."
The travel ban, which the Supreme Court allowed to take effect in
December, has been widely criticised by refugee and human rights groups.
Chief Justice John Roberts wrote the opinion, which said the travel ban was "squarely within the scope of Presidential authority".
He also rejected arguments that the ban discriminated against Muslims.
"The Proclamation is expressly premised on legitimate purposes:
preventing entry of nationals who cannot be adequately vetted and
inducing other nations to improve their practices," Chief Justice
Roberts wrote. "The text says nothing about religion."
Shortly after the Supreme Court released its decision, President Donald Trump shared the news from his Twitter account.
Justice Ruth Bader Ginsburg joined Justice Sonia Sotomayor in the
dissenting opinion, which argues the court failed to uphold the
religious liberty guaranteed by the first amendment of the US
constitution.
"It leaves undisturbed a policy first advertised
openly and unequivocally as a 'total and complete shutdown of Muslims
entering the United States' because the policy now masquerades behind a
facade of national-security concerns," Justice Sotomayor wrote.
The dissent also states that "a reasonable observer would conclude that [the ban] was motivated by anti-Muslim animus".
What does this ruling mean?
The
travel ban has been in place since December, when the Supreme Court
ruled that it could go into full effect, pending legal challenges.
The ban prevents most immigrants, refugees and visa holders from
five Muslim-majority countries - Iran, Libya, Somalia, Syria and Yemen -
as well as North Korea and Venezuela from entering the US.
But the restrictions on North Korea and Venezuela were not part of the legal challenge.
The
ban allows for waivers on a case-by-case basis, but applicants who
cannot afford an attorney to go through the waiver process will likely
be unable to immigrate to the US, immigration advocates say.
Justice
Stephen Breyer noted in his dissenting opinion that the State
Department reported that only two waivers were approved out of 6,555
applicants during the first month of the travel ban.
The high court has been issuing a number of decisions this week,
including a ruling against a California law that required clinics to
inform women of the availability of abortions paid for by the state.
The Court ruled that the law violated the free speech rights of Christian facilities.
Third time's a charm
Analysis by Anthony Zurcher, BBC News - at the scene
Despite
the controversial nature of Donald Trump's travel ban, there were more
abortion rights activists outside the Supreme Court on Tuesday morning
than immigration protesters.
Perhaps it's because abortion has
been a contentious legal battle for decades, while the president's
travel directive had been in effect, and out of the headlines, for
months.
Attention in recent weeks has been on migrants coming
across the southern US border, not visitors and prospective residents
from countries like Libya, Iran, Yemen and Syria.
Nevertheless,
this marks a significant victory for Mr Trump - and for presidential
power to set immigration policy in general - albeit by the narrowest of
margins.
The five court justices said they took the president's
order on its face, and separated it from his more bombastic anti-Muslim
comments made on the presidential campaign trail and via Twitter.
The
travel ban was implemented haphazardly at the start of the Trump
administration and faced repeated setbacks from the US legal system. In
the end, however, the president got his way - or at least enough of his
way to claim success.
The third time turned out to be the charm.
What's the reaction?
The White House issued a statement saying the ruling was "a tremendous victory for the American People and the Constitution".
"In
this era of worldwide terrorism and extremist movements bent on harming
innocent civilians, we must properly vet those coming into our
country."
Immigration lawyer Cyrus Mehta told the BBC that the
majority opinion "gave in to President Trump's hate and bigotry and will
be viewed as a blemish".
