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The positive tests come just hours after it emerged senior aide Hope Hicks, who travelled with Mr Trump several times this week, came down with the virus.
The US President confirmed the news on Twitter, while the First Lady said they were “feeling good”.
Mrs Trump said she had postponed all upcoming engagements, but the president’s doctor said Mr Trump would “carry out his duties without disruption while recovering,”
Mr Trump wrote on Twitter: “Tonight, @FLOTUS and I tested positive for COVID-19. We will begin our quarantine and recovery process immediately. We will get through this TOGETHER!”
The First Lady added: “As too many Americans have done this year, @potus & I are quarantining at home after testing positive for COVID-19.
“We are feeling good & I have postponed all upcoming engagements. Please be sure you are staying safe & we will all get through this together.”
Mr Trump is 74 years old, putting him at higher risk of serious complications from a virus that has now killed more than 200,000 people in the US.
The president is now expected to be in quarantine for some two weeks while facing treatment for the disease.
Sean Conley, physician to the president, said: “The President and First Lady are both well at this time, and they plan to remain at home within the White House during their convalescence.
“The White House medical team and I will maintain a vigilant watch, and I appreciate the support provided by some of our our country’s greatest medical professionals and institutions.
“Rest assured I expect the President to continue carrying out his duties without disruption while recovering, and I will keep you updated on any future developments.”
The stunning development comes a month before the US election on November 3