The high court will rule on whether the president exceeded his powers and engaged in religious discrimination in the third version of the ban.
Lower courts in California, Hawaii and other states have repeatedly ruled that Trump's order targets Muslims in violation of the US Constitution.
"We have always known this case would ultimately be decided by the United States Supreme Court," said state Attorney General Doug Chin of Hawaii, which has repeatedly fought the travel bans.
"This will be an important day for justice and the rule of law. We look forward to the Court hearing the case."The conservative-tilting court last month rejected calls for a freeze
on the ban, which targets visitors from Chad, Iran, Libya, Somalia, Syria and Yemen, allowing Trump to implement it while it was being challenged in lower courts.
The US administration has rewritten the ban twice, adding more national security justifications in the latest iteration in September and including citizens of North Korea and Venezuela to counter the argument the government was singling out Muslim countries.
National security, not religion
Trump's initial travel ban, which he first sought to implement a week after he took office, triggered chaos at US airports, with travelers detained upon arrival, and nationwide protests against a measure seen as discriminatory - though Trump said it aimed to keep out extremists.
Court challenges have seized upon Trump's repeated comments against Muslims, starting with his campaign vow to ban them
from entering the country, to make the case that they were the intended target.
The first ban was quickly blocked in court, as was a modified version removing Iraq from the list of countries.
Regarding the third version
, critics noted that the United States welcomed no more than a handful of annual visitors from North Korea, and in Venezuela's case, the ban was made specific to a number of high-ranking officials in a government already facing US sanctions.
One key difference in the latest version of the ban was that it was open-ended, whereas the previous two versions were set for 90 days, ostensibly for the government to review security threats from the countries.
The Supreme Court will review those arguments, but also whether Trump has the executive power to order such a ban.
"Every version of the ban has been found unconstitutional, illegal, or both by federal trial and appellate courts," said Omar Jadwat, director of the Immigrants' Rights Project at the American Civil Liberties Union, which has supported Hawaii in its court challenge.
"The Supreme Court can and should put a definitive end to President Trump's attempt to undermine the constitutional guarantee of religious equality and the basic principles of our immigration laws, including their prohibition of national origin discrimination," Jadwat said.