Mr Raab arrived at No 10 on Tuesday morning and will later chair the government's daily Covid-19 meeting.
He said earlier there was an "incredibly strong team spirit" behind the prime minister and that he and his colleagues were making sure they implemented plans Mr Johnson had instructed them to deliver "as soon as possible".
Former Conservative leader Sir Iain Duncan Smith said the government will "continue to work" as decisions are made collectively by the cabinet.
He also sounded a warning to people who have broken social distancing guidelines, saying "if the most powerful man in Britain can come down with this, so can you".
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.
Mr Johnson's friend and former direction of communications Will Walden told BBC Radio 4's Today programme Mr Johnson is "far fitter than he looks".
"He will whip anybody's backside on a tennis court, he runs regularly, he doesn't smoke, he drinks moderately.
"So I think if anyone is in a good position both physically and mentally to fight off the disease then the prime minister is that person."
After very, very little information was shared today, the prime minister was taken into intensive care at around 19:00 BST.
We've been told he is still conscious, but his condition has worsened over the course of the afternoon.
And he has been moved to intensive care as a precaution in case he needs ventilation to get through this illness.
The statement from Downing Street makes clear he is receiving excellent care and he wants to thank all of the NHS staff.
But something important has changed, and he has felt it necessary to ask his foreign secretary to deputise for him where needs be.
That is a completely different message from what we have heard over the past 18 hours or so, where it was continually "the prime minister is in touch" and "he is in charge" - almost like everything is business as usual.
But clearly being in intensive care changes everything.