Johnson, who was admitted to intensive care in a London hospital earlier this year with the novel coronavirus, is well and does not have any symptoms, a spokesman for the prime minister said on Sunday.
"He will carry on working from Downing Street, including on leading the Government's response to the coronavirus pandemic", the Downing Street spokesman added.
The announcement came after Johnson met a small group of MPs at Downing Street on Thursday for around 35 minutes, including one who subsequently developed symptoms of Covid-19 and has now tested positive.
Mr Cummings has been at the Premier's side since he took power in July last year, and masterminded the successful Brexit referendum campaign that catapulted Mr Johnson into the front rank of British politics three years earlier.
He told BBC Radio there have been more than 25 confirmed cases of COVID-19 reinfection globally, but that he thought the actual rate of reinfection is "quite a lot higher than that, but not enormous".
Gavin Barwell, former chief of staff to then-prime minister Theresa May, tweeted: "Big moment: Boris now has an opportunity to get a more harmonious, effective Downing Street operation (like he had at City Hall); improve relations with the parliamentary party; and lead a less confrontational, more unifying government that better reflects his own character".
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Johnson said on Sunday he had been told by the NHS Test & Trace scheme to self-isolate for two weeks.
Johnson's spokesperson stressed late last week that the prime minister had not been distracted by the row and is "fully focused" on grappling with coronavirus-related issues.
"On Friday I lost my sense of taste at the same time my wife had a bad headache".
He said: "Breakfast with the PM".
Green MEP Phillipe Lamberts, a member of the EU Parliament's Brexit Steering Group, said that Cumming's departure was "probably the sign that Johnson has begun his U-turn and will, in the end, accept EU conditions".
Downing Street said the measures ahead would include plans to tackle the coronavirus outbreak, moves for "levelling up" across the country, and education and environmental investment initiatives.
The dramatic exit of Boris Johnson's senior adviser Dominic Cummings will have no impact on crucial Brexit negotiations, Environment Secretary George Eustice said.