However, none of them will need to self-isolate as they will participate in a daily contact test pilot project instead.
Health Secretary Sajid Javid confirmed on Saturday morning that he had tested positive for the virus and said his symptoms were “mild”.
Ministers were waiting to see if they would be identified as someone who had come into close contact with Mr Javid.
A No.10 spokesperson confirmed on Sunday morning that Boris Johnson and Rishi Sunak had been contacted by NHS Test and Trace.
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The statement said: “They will participate in the daily contact test pilot to allow them to continue working from Downing Street.
“They will only conduct essential government business during this time. “
Downing Street is one of the few selected organizations covered by a workplace pilot project, alongside Networks Rail, TFL and Heathrow Airport.
Participants should always isolate themselves when not at work.