The 55-year-old prime minister sent a video message via Twitter, confirming the diagnosis.
"Over the last 24 hours I have developed mild symptoms and tested positive for coronavirus,” he said.
"I am now self-isolating, but I will continue to lead the government's response via video-conference as we fight this virus."
He added: "Together we will beat this. #StayHomeSaveLives."
A Downing Street spokesman said Mr Johnson had been tested on the suggestion of his chief medical officer Professor Chris Whitty, having been experiencing "mild symptoms" yesterday.
"The test was carried out in No 10 by NHS staff and the result of the test was positive.
"In keeping with the guidance, the prime minister is self-isolating in Downing Street