The designation allows Musk, the world's richest man, to work for the federal government but potentially avoid disclosure rules about conflicts of interest and finances that apply to regular government employees.
Musk still runs electric car company Tesla and aerospace company SpaceX while chairing Trump's cost-cutting effort called the Department of Government Efficiency. As CEO of SpaceX, Musk oversees the company's contracts with the Pentagon and intelligence community that are worth billions of dollars.
White House press secretary Karoline Leavitt said Musk is classified as a "special government employee." A second senior White House official said Musk is not receiving a government pay cheque and is following the law.
Special government employees are appointed to their positions for no more than 130 days, but Trump has not said how long Musk's position will last.
Musk, who has promised "mass head-count reductions" across the federal bureaucracy, has drawn wide scrutiny in recent days as his team has been given access to or has taken control of numerous government systems. His moves have struck fear into the government workforce and caused chaos inside some agencies.
Reuters reported on Friday that aides to Musk charged with running the US government human resources agency have locked career civil servants out of computer systems that contain the personal data of millions of federal employees, according to two agency officials.
Musk also has targeted the US Agency for International Development for closure, calling the humanitarian agency a left-wing organisation unaccountable to the White House.
Democratic politicians have decried what they characterise as an unelected billionaire amassing too much power over the federal government.
US President Donald Trump has praised Musk as having "a good, natural instinct". (AP PHOTO)
Trump, who officials say has entrusted Musk with overseeing the revamp of USAID, defended Musk but said there are limits to what his adviser can do.
"Elon can't do and won't do anything without our approval, and we'll give him the approval, where appropriate; where not appropriate, we won't. But he reports in," Trump said to reporters.
"It's something that he feels very strongly about, and I'm impressed, because he's running, obviously, a big company," Trump added.
"If there's a conflict, then we won't let him get near it. But he does have a good, natural instinct. He's got a team of very talented people."
Since taking office, Trump has embarked on a massive government makeover, firing and sidelining hundreds of civil servants in his first steps toward downsizing the bureaucracy and installing more loyalists.
A separate US official said Trump is not closely monitoring Musk's moves but is being kept up to date. "He's read in," the official said of Trump's awareness of Musk's activities.
Kathleen Clark, a government ethics professor at the Washington University School of Law, said most special government employees are not required to publicly file financial disclosures.
Musk's new designation could be a way to avoid disclosing publicly his finances and his many conflicts, she said.