Mr Johnson has mild symptoms and will self-isolate in Downing Street.
“He was tested for coronavirus on the personal advice of England’s chief medical officer, Professor Chris Whitty,” a statement said.
He will remain in control of the government’s dealing of the crisis, the statement added.
“The test was carried out in No 10 by NHS staff and the result of the test was positive,” the statement added.
“In keeping with the guidance, the Prime Minister is self-isolating in Downing Street.