The 5-4 decision is the court's first substantive ruling on a Trump administration policy.
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Chief Justice John Roberts wrote the majority opinion, joined by his four conservative colleagues.
Roberts wrote that presidents have substantial power to regulate immigration. He also rejected the challengers' claim of anti-Muslim bias.
The court may have signaled its eventual approval in December, when the justices allowed the policy to take full effect even as the court fight continued and lower courts had ruled it out of bounds.
Roberts was careful not to endorse either Trump's provocative statements about immigration in general and Muslims in particular.
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"We express no view on the soundness of the policy," Roberts wrote.
Justice Sonia Sotomayor wrote in a dissent that based on the evidence in the case "a reasonable observer would conclude that the Proclamation was motivated by anti-Muslim animus." She said her colleagues arrived at the opposite result by "ignoring the facts, misconstruing our legal precedent, and turning a blind eye to the pain and suffering the Proclamation inflicts upon countless families and individuals, many of whom are United States citizens."
Justices Stephen Breyer, Ruth Bader Ginsburg and Elena Kagan also dissented.