Johnson was admitted to St Thomas” Hospital on Sunday, on the advice of his doctor, after continuing to have a cough and high temperature 10 days after testing positive for the virus, the BBC reported.
The Prime Minister was given oxygen before being taken to intensive care on Monday.
The spokesman said that Johnson was in “good spirits” on Wednesday as he continued to receive standard oxygen treatment.
He was breathing without any assistance, such as mechanical ventilation or non-invasive respiratory support.
The spokesman added that he was not working but could contact those he needed to.
The Queen and other senior royals sent messages to Johnson”s family and his pregnant fiancee, Carrie Symonds, saying they were thinking of them, and wished the Prime Minister a full and speedy recovery.
Foreign Secretary Dominic Raab, who is deputising for Johnson, said on Tuesday he was “confident” the PM would recover from this illness, describing him as a “fighter”, the BBC reported.
The news of Johnson”s improvement comes as the number of confirmed coronavirus cases in the UK increased to 61,474 as of Wednesday, with death toll now standing at 7,097.
On Wednesday, the Downing Street said a review of lockdown rules would go ahead next week, but the public must “stick with” the measures at what was a “critical time”.
A ban on public gatherings of more than two people and the closure of shops selling non-essential goods were among the series of restrictions announced by Johnson on March 23 to tackle the spread of coronavirus.
Downing Street said a relaxation of the rules would be considered “on or around” the three-week mark on April 13.
According to the government”s coronavirus legislation, the health secretary must review the need for restrictions at least once every 21 days, with the first review to be carried out by April 16.
Mayor of London Sadiq Khan told the BBC: “I think we”re nowhere near lifting the lockdown.
“We think the peak – which is the worst part of the virus – is still probably a week and a half away.”