President Trump calledpolicy a "clear victory" for national security.
"As President, I cannot allow people into our country who want to do us harm. I want people who can love the United States and all of its citizens, and who will be hardworking and productive," said Mr. Trump in a statement.
He added, "Today's ruling allows me to use an important tool for protecting our Nation's homeland. I am also particularly gratified that the Supreme Court's decision was 9-0."
The opinion in the case was unsigned, meaning that it's not known what the breakdown was on the justices' vote. However, there were also no dissents, and that suggests that the decision to take the case is likely to have been unanimous.
Justices Clarence Thomas, Samuel Alito and Neil Gorsuch felt the partial reinforcement of the travel ban did not go far enough, according to a separate opinion written by Thomas and joined by Alito and Gorsuch. The three think the ban should have been reinstated in its entirety for the six countries in the ban.
Mr. Trump's comments come as the Supreme Court announced its decision on the final day of the high court's opinions. The court also moved to lift an injunction blocking the president's travel policy, effectively allowing the ban to go into effect for the six countries.
The policy would impose a 90-day pause in travel from citizens of Iran, Libya, Somalia, Sudan, Syria and Yemen and into the U.S..
The travel ban will now be argued in October.
Mr. Trump's son Donald Jr. also applauded the Court's move and criticized one lower court decision to block the ban.
The ACLU,over the ban, quickly responded to the highly anticipated decision, warning the president "we'll see him court."
Attorney General Jeff Sessions echoed Mr. Trump's statements of protecting national security, saying in a written statement, that in light of recent Islamic State of Iraq and Syria (ISIS) inspired threats, it is "crucial to properly vet those seeking to coming to America" adding "failure to do so puts us all in danger."
Sessions added "The Court's decision recognizes that the Executive has the responsibility to protect the safety and security of the American people under the Constitution of the United States and its laws. The judiciary serves, pursuant to their oath, under the same Constitution and these same laws. This case raises profound questions about the proper balance of these constitutional powers, and we are eager to advance our views on these important issues."
Meanwhile, Jay Sekulow, a member of Mr. Trump's legal team, told Fox Business Network that the legal decision should be viewed as a "big win" for the White House.
"The only thing they did not put the ban in place for, the travel restrictions for, was a very limited situation with the mother of the U.S. citizen. So, it's a very narrow carve out, but the timing the procedures, the 90 day- the waiting period, the hold back, all of those have been deemed constitutional," said Sekulow on Fox Business Network's "Varney & Co."
The country had been waiting for the court to make its decision public about the biggest legal controversy in the first five months of Mr. Trump's presidency. The Supreme Court usually saves its most important decisions for the final day of the term. The issue has been tied up in the courts since his original order in January sparked confusion and widespread protests just days after he took office.
It would have taken five votes to reinstate the ban, but it only took four to set the case for argument. Justice Neil Gorsuch, Mr. Trump's nominee who was confirmed in April, took part in the highest-profile issue yet in his three months on the court.
CBS News' Jan Crawford contributed to this report.