The prime minister and chancellor will not be self-isolating after contact with Health Secretary Sajid Javid, who has tested positive for coronavirus.
Downing Street said the pair would take part in a pilot programme, where daily tests replace self-isolation.
They will have to self-isolate when not working and will only conduct essential business, a spokesman said.
Labour said the public would think this means there is “one rule for them and another for the rest of us”.
Mr Javid tested positive on Saturday morning after a meeting at Downing Street the day before, and both Boris Johnson and Rishi Sunak were contacted by NHS Test and Trace as his contacts.
Downing Street is among 20 private and public sector organisations – including Network Rail, Transport for London and Border Force – taking part in a pilot where close contacts of Covid cases take daily tests.
Workplaces need a testing system in place for asymptomatic people and individuals taking part must self-isolate when not working.
Number 10 said: “They will be participating in the daily contact testing pilot to allow them to continue to work from Downing Street. They will be conducting only essential government business during this period.”
Case numbers are continuing to rise ahead of the lifting of legal rules on social contact in England on Monday, and businesses have raised concerns about staff shortages due to the numbers of people self-isolating.
More than half a million alerts telling people to self-isolate were sent by the NHS Covid-19 app in England and Wales in the first week of July, with unions saying it was causing “havoc” on production lines.
Opposition parties criticised the decision to allow the prime minister and chancellor to escape the normal self-isolation requirements.
Labour’s shadow health secretary Jonathan Ashworth told the BBC’s Andrew Marr Show parents whose children were missing school or businesses short of workers would be thinking “it’s one rule for them and another for the rest of us”, with politicians having access to “VIP testing”.
He said ending almost all legal restrictions on Monday while cases surge is “reckless, like putting your foot down on the accelerator while taking your seat belt off”.
Liberal Democrat leader Sir Ed Davey said: “How about the school teachers, transport workers and health workers getting a chance to be part of this test pilot, or is it only for the privileged few?”