However, Chief Justice John Roberts in a dissent called the project "likely unlawful".
The court ruled 5-4 to grant the administration's request to block a lower court's order halting above-ground construction of the $US400 million ($A559 million) ballroom while a lawsuit by a historic preservation group seeking to stop the project proceeds.
The National Trust for Historic Preservation sued last year after the administration tore down the White House East Wing and began building a 8360 square metre ballroom without seeking specific approval from Congress.
Trump has said the ballroom will be "the greatest of its kind ever built".
Monday's ruling, lauded by Trump, was powered by five of the court's six conservative justices.
They wrote that the plaintiffs in the case, the nonprofit National Trust for Historic Preservation, lacked the necessary legal standing to sue.
They also said the government would likely suffer "irreparable harm" if the project were blocked, citing national security concerns.
Roberts was the only conservative justice to dissent. He was joined in his dissent by the court's three liberal justices.
The ballroom construction is "likely unlawful," Roberts wrote, noting that Congress has "plenary constitutional authority over the District of Columbia and federal property" and that it has prohibited structures from being built on federal government grounds in Washington, DC, without its authorisation.
"The ballroom is a building or structure being erected on federal park grounds - President's Park - in the District of Columbia. Yet Congress has not passed any law resembling 'express authority' for the Executive's construction of it," Roberts wrote.
Trump in a social media post welcomed the ruling and called the legal challenge baseless.
"I am pleased to report that the United States Supreme Court has just ruled in favor of the Ballroom/Military Complex being built without any further contingency, doubt, or threat. We are living in the Golden Age of America, and this Building will be one of the Greatest ever constructed in Washington, D.C.," Trump wrote.
Roberts on August 21 had imposed a brief administrative stay to give the court additional time to consider the Trump administration's request.
In an August 14 filing to the Supreme Court, Justice Department lawyers echoed the Republican president's contention that the project is a security necessity, citing assassination attempts against the president and other recent threats.
"This case involves an extraordinary and unlawful injunction that will halt the ongoing construction of the integrated military complex, including a totally secure ballroom space, at the East Wing of the White House, which is vitally required by national security," they wrote.
The project combines the above-ground ballroom with an extensive underground complex.
Trump has said the project includes bomb shelters, medical facilities, shielding from drones and missiles and other security features that are "all tied together as one big, expensive and very complex unit".
On August 7, the US Court of Appeals for the District of Columbia Circuit in a 2-1 ruling upheld US District Judge Richard Leon's order directing the administration to halt above-ground construction.
"Each President is a temporary tenant, not the owner, of the White House," and cannot fundamentally reshape it without congressional approval, the DC Circuit's ruling stated.
The district judge's order did not permanently bar construction of a ballroom.
It blocked above-ground efforts while allowing below-ground construction to continue, as well as work deemed "strictly necessary" for the safety and security of the White House. In its ruling, the DC Circuit said national security arguments "are not an automatic get-out-of-law-free card".
The Justice Department said in its August 14 filing that the overall East Wing project - including both the underground facilities and the above-ground ballroom - is 65 per cent complete.
The Supreme Court, with its 6-3 conservative majority, has frequently ruled in favour of Trump in his second term in office, with some notable exceptions, as he has pushed to expand his powers in domestic affairs and foreign policy.
