The prime minister is understood to be conscious and was moved at about 7pm as a precaution should he require ventilation to aid his recovery.
Foreign secretary Dominic Raab will “deputise where necessary” while the prime minister is battling Covid-19, a No.10 spokesperson said.
Asked by the BBC on Monday night if he was confident the government is “under control”, Raab said: “There’s an incredibly strong team spirit behind the prime minister, and [we are] making sure that we get all of the plans the prime minister’s instructed us to deliver to get them implemented as soon as possible.
“And that’s the way it will bring the whole country through the coronavirus challenge that we face right now.”
Buckingham Palace said the Queen is being kept informed about his condition.
Johnson, 55, was admitted to St Thomas’s Hospital in Westminster on Sunday after his coronavirus symptoms persisted for 10 days.
But, having been in hospital for tests and observation, his doctors advised that he be admitted to intensive care.
US president Donald Trump offered his support for Johnson at a White House briefing.
“I want to send best wishes to a very good friend of mine, and a friend to our nation, prime minister Boris Johnson,” Trump said.
“We are very saddened to hear that he was taken into intensive care this afternoon a little while ago. And Americans are all praying for his recovery.
“He has been a really good friend. Very strong. Resolute, he does not quit. Does not give up.”
The spokesperson said: “Since Sunday evening, the prime minister has been under the care of doctors at St Thomas’s Hospital, in London, after being admitted with persistent symptoms of coronavirus.
“Over the course of this afternoon, the condition of the prime minister has worsened and, on the advice of his medical team, he has been moved to the intensive care unit at the hospital.
“The PM has asked foreign secretary Dominic Raab, who is the first secretary of state, to deputise for him where necessary. The PM is receiving excellent care, and thanks all NHS staff for their hard work and dedication.”
Raab had earlier faced questions at the government’s daily coronavirus press conference about Johnson’s apparent decision to keep running the government from his hospital bed instead of handing over the reins.
Following the announcement, politicians from around the world and across the political spectrum offered their support for the PM.
Labour leader Sir Keir Starmer tweeted: “Terribly sad news. All the country’s thoughts are with the prime minister and his family during this incredibly difficult time.”
Earlier on Monday, Johnson tweeted: “Last night, on the advice of my doctor, I went into hospital for some routine tests as I’m still experiencing coronavirus symptoms. I’m in good spirits and keeping in touch with my team, as we work together to fight this virus and keep everyone safe.
“I’d like to say thank you to all the brilliant NHS staff taking care of me and others in this difficult time. You are the best of Britain.”
On Saturday it was revealed Johnson’s fiancée Carrie Symonds has also been suffering from coronavirus symptoms.
The 32-year-old conservationist, who is pregnant with the couple’s first child, said she had spent the past week in bed, but had not been tested for the virus.