Deputy White House press secretary Hogan Gidley said the valet, who is also a member of the U.S. Navy, exhibited symptoms on Wednesday.
"We were recently notified by the White House Medical Unit that a member of the United States Military, who works on the White House campus, has tested positive for coronavirus," Gidley said said in a statement. "The president and the vice president have since tested negative for the virus and they remain in great health."
Gidley added that Trump and Vice President Mike Pence each were tested immediately after the valet was diagnosed.
"As our nation heals, our spirit has never been stronger!" Trump tweeted, acknowledging an order he issued proclaiming the first Thursday in May a National Day of Prayer.
The president spoke by phone Thursday with Russian President Vladimir Putin to commemorate the 75th anniversary of Victory in Europe Day, during which the two leaders discussed efforts to end the coronavirus crisis. The White House said they also talked about arms control and "other bilateral and global issues."
In New York, Gov. Andrew Cuomo has extended a moratorium on evictions until at least August, barring landlords from kicking out tenants who are facing economic hardship due to the health crisis. It was set to expire in June, but Cuomo's extension postpones the deadline to Aug. 21.
Under the extension, tenants will be allowed to use their security deposits to pay rents.
"We are helping the landlords also, but on a human level, I don't want to see people and their children being evicted at this time through no fault of their own," he said.
Also at his briefing Thursday, he said the latest death toll in the state was 231. So far, nearly 21,000 New Yorkers have died of the disease.
Cuomo said hospitalizations are down "significantly."
"The downside of the mountain is a much more gentle slope than what we went through going up the mountain," he said. "We wish it was a steeper decline, but it's not."
Earlier, New York City Mayor Bill de Blasio said new hospital and ICU admissions in the city have also declined.
Since the start of the pandemic, more than 73,000 patients have died of the virus and 1.23 million have tested positive, according to Johns Hopkins University.
In Pennsylvania, attorneys for the family of a Philadelphia meatpacker who died of COVID-19 sued his employer for wrongful death and negligence -- the first of what could be many legal actions to come against U.S. meat processors that stayed open during the pandemic.
The lawsuit says the company failed to protect workers with proper equipment and started a special "Saturday Kill" program to meet increased demand.
More than 9,000 people at dozens of U.S. meatpacking plants have been sickened by the coronavirus.