Boris Johnson and Health Secretary Matt Hancock have tested positive for coronavirus.
The Prime Minister said he will continue to lead the "national fightback" against the virus despite being forced to self-isolate.
The 55-year-old PM said he had mild symptoms – including a high temperature and persistent cough – and will work from his flat in Number 11 for the next week.
Nearly two hours after Mr Johnson announced he had tested positive for Covid-19, Mr Hancock tweeted that he too had mild symptoms and was working from home and self-isolating.
He said: "Fortunately for me the symptoms so far have been very mild so I've been able to carry on with the work driving forward the UK response."
Mr Johnson noticed that he had mild symptoms on Thursday afternoon and received the test results at midnight, Downing Street said.
His pregnant partner Carrie Symonds is not believed to be with the PM, and is reportedly isolating alone in Camberwell, south London, with the couple's dog, Dilyn.
Following medical advice, I was advised to test for #Coronavirus.
I've tested positive. Thankfully my symptoms are mild and I'm working from home & self-isolating.
— Matt Hancock (@MattHancock) March 27, 2020
In a video message posted to Twitter, Mr Johnson 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 fightback against coronavirus.
"I want to thank everybody involved and, of course, our amazing NHS staff."
The Prime Minister's spokesman told a Westminster briefing that the PM dialled into the daily "war cabinet" meeting from Number 11, and will continue to do so while he is self-isolating.
"He will do the same things but that will be done exclusively via teleconferencing on his part," the spokesman said.
However, Mr Johnson will not appear at Friday's press conference.
Meals and work will be left outside the PM's flat, while the doors between Number 10 and Number 11 have been closed off to all other staff who work in the building.
A spokesman for the Chancellor said Rishi Sunak has not had any symptoms and therefore has not been tested for coronavirus and is not self-isolating.