Johnson, 55, was taken to St Thomas' hospital, in London, on Sunday - 10 days after testing positive for the virus.
He spent three nights in intensive care before returning to a ward on Thursday, the BBC reported.
A Downing Street statement said the Prime Minister would continue his recovery at his country residence, Chequers.
"On the advice of his medical team, the PM will not be immediately returning to work. He wishes to thank everybody at St Thomas' for the brilliant care he has received."
"All of his thoughts are with those affected by this illness," the statement said.