The U-turn comes a day after health minister Sajid Javid said he had tested positive for COVID-19 and at a time when the government's coronavirus response is under intense scrutiny.
Finance minister Rishi Sunak - who was also in close contact with Javid - will self-isolate as well.
Almost all remaining restrictions in England will be lifted on Monday despite a surge in infections as politicians put their faith in the advanced vaccine program.
Cases are rising by more than 50,000 a day and hundreds of thousands of Britons are being asked to self isolate for 10 days, causing havoc for employers and parents, prompting train cancellations and forcing some businesses to close their doors.
The government had initially announced that Johnson and Sunak had been exposed to a person with COVID-19 and would take part in a trial scheme that allowed them to keep working instead of self-isolating.
But less than three hours later that decision had been reversed after a flurry of criticism from voters, political opponents and business owners.
"We did look briefly at the idea of us taking part in the pilot scheme... but I think it's far more important that everybody sticks to the same rules," Johnson said in a video message from his country residence, where he will isolate until July 26.
Ahead of the country's reopening, Johnson used his video message to plead with the public to take a cautious approach to the change of rules.
"Please, please, please, be cautious," he said.