In a video on Monday, he urged others to "follow the rules" and self-isolate if contacted by NHS Test and Trace.
The prime minister said he was "pinged" by the scheme on Sunday.
On Thursday Mr Johnson spent about 35 minutes with Tory MP Lee Anderson, who lost his sense of taste the next day.
The PM's period of isolation begins as the government prepares a policy relaunch after fierce internal rows and departures from No 10.
Downing Street said a series of "critical announcements" would this week detail Mr Johnson's "ambitions for the United Kingdom".
Mr Johnson will chair "key Covid meetings" and work with Chancellor Rishi Sunak to devise the upcoming spending review with an aim to fulfil his promise to "build back better".
The PM will now be working from his flat at Downing Street.
This is why you can eat in a restaurant but can’t have Thanksgiving.