"I will be departing on January 20th," Ambassador Mark Gilbert said in a Twitter message to Reuters.
The mandate was issued "without exceptions" through an order sent in a State Department cable on December 23, Gilbert said.
He was confirming a report in the New York Times, which quoted diplomatic sources as saying previous US administrations, from both major political parties, have traditionally granted extensions to allow a few ambassadors, particularly those with school-age children, to remain in place for weeks or months.
Officials from the State Department and Trump's transition team were was not immediately available for comment.
The order threatens to leave the United States without Senate-confirmed envoys for months in critical nations like Germany, Canada and Britain, the New York Times reported.
A senior Trump transition official told the newspaper there was no ill will in the move, describing it as a simple matter of ensuring Obama's overseas envoys leave the government on schedule, just as thousands of political aides at the White House and in federal agencies must do.
Trump has taken a strict stance against leaving any of Obama's political appointees in place as he prepares to take office on January 20, aiming to break up many of his predecessor's signature foreign and domestic policy achievements, the newspaper said.
Diplomats told New York Times the order has thrown their personal lives into a tailspin, leaving them scrambling to secure living arrangements and acquire visas allowing them to stay in their countries so their children can remain in school.