Mr Johnson said he had developed mild symptoms over the past 24 hours, including a temperature and cough.
He is self-isolating in Downing Street but said he will “continue to lead the government’s response via video-conference as we fight this virus”.
Mr Johnson was last seen on Thursday night, clapping outside No 10 as part of a nationwide gesture to thank NHS staff and carers.
In a video on his Twitter account, Mr Johnson, 55, said: “I’m working from home and self-isolating and that’s entirely the right thing to do.
“But, be in no doubt that I can continue thanks to the wizardry of modern technology to communicate with all my top team to lead the national fight-back against coronavirus.
“I want to thank everybody involved and, of course, our amazing NHS staff.”
“So thank you to everybody who’s doing what I’m doing, working from home to stop the spread of the virus from household to household,” he added.
“That’s the way we’re going to win.”
Mr Johnson was tested at No 10 by NHS staff, on the personal advice of England’s chief medical officer, Prof Chris Whitty, Downing Street said.
He remains in charge of the government’s handling of the crisis and is understood to have chaired a phone call on Friday morning.
Earlier this week the prime minister’s spokesman said if Mr Johnson was unwell and unable to work, Foreign Secretary Dominic Raab, as the first secretary of state, would stand in.
Source: BBC