The top court stayed a decision by a lower court two days earlier that had blocked the restrictions, which require migrants seeking asylum in the United States to make their request in a country along their route.
Justice Sonia Sotomayor, dissenting from the Supreme Court's decision, wrote that: "Once again the Executive Branch has issued a rule that seeks to upend longstanding practices regarding refugees who seek shelter from persecution."
Trump took to Twitter to hail the move, saying: "BIG United States Supreme Court WIN for the Border on Asylum!"
The policy is among a host of measures Trump has taken in a bid to stem the flow of Central American migrants trying to cross into the US from Mexico and request asylum.
The Pentagon said Tuesday that it will keep up to 5,500 troops deployed at the southern US border for the coming year to help combat illegal immigration.
It has also announced that it would divert $3.6 billion in funds for construction of an anti-migrant wall on the frontier, which Trump promised that Mexico would pay for.
The diversion of the Pentagon funds to border wall construction was justified under a controversial emergency declaration made by Trump after Congress repeatedly denied the president money for the project.