"The PM was with Ms Symonds this morning for the birth of their son and is now back at work in Number 10".
Mr Johnson said: "At no stage has our NHS been overwhelmed, no patient went without a ventilator, no patient was deprived of intensive care, we have five of the seven projected Nightingale wards".
Both mother and baby are "doing very well", and it is understood that despite having recently recovered from the novel coronavirus, Johnson was present at the birth.
"The PM and Ms Symonds would like to thank the fantastic NHS maternity team", Downing Street said.
While the Prime Minister did not put a clear date on when lifting the lockdown might come, the government's spokesman gave some indications earlier in the day when they refused to rule out it lasting until June.
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The couple had announced their engagement at the end of February, when it was also revealed that they were expecting their first baby in the summer.
Saying the coming stages would require "collective discipline" on behalf of the United Kingdom and that the country would have to continue to pull together in a way "few of us have seen in our lifetimes", Mr Johnson nevertheless noted that much had already been achieved. Ms Symonds (32) also suffered symptoms.
The Queen has sent a private message of good wishes to congratulate the couple on the birth of their son, Buckingham Palace said.
Politicians began issuing congratulations to the couple - among them finance minister Rishi Sunak and opposition Labour party leader Keir Starmer.
The new arrival is the third baby born to a serving prime minister in recent United Kingdom history. Earlier this month, she announced that she was feeling better.
In 2013, when Mr Johnson was mayor of London, appeal court judges ruled that the public had the right to know he had an extra-marital affair with a woman who gave birth to his daughter.