The Prime Minister will not take time off work until later in the year, his official spokesman said, as congratulations and well-wishes poured in from across the political divide and around the globe.
Both Ms Symonds and the baby were doing well, Foreign Secretary Dominic Raab told the daily coronavirus press briefing in Downing Street.
The news comes just weeks after the Prime Minister’s brush with death, having spent three days in intensive care fighting off Covid-19. Ms Symonds also had to self-isolate with symptoms of the disease.
Mr Johnson, 55, and Ms Symonds, 32, announced in February that they were expecting a baby in “early summer”, and that they had become engaged at the end of last year.
It is understood Mr Johnson was present throughout the birth at an unnamed London hospital.
Mr Johnson has previously suggested he intends to take paternity leave. His spokesman said: “The Prime Minister was with Ms Symonds this morning for the birth of his son and is now back at work in Number 10.
“Later in the year he will take a short period of paternity leave.”
Earlier, a Number 10 spokeswoman passed on the Prime Minister and Ms Symond’s thanks to “the fantastic NHS maternity team”.
The couple are now both in Downing Street after Ms Symonds joined Mr Johnson during his two-week convalescence at Chequers.
He did not appear at Prime Minister’s Questions in the Commons yesterday, which was taken by Mr Raab.
First Minister Nicola Sturgeon responded to the announcement on twitter, posting: “Some good news - sending congratulations to Carrie and the PM. And wishing health and happiness to the wee one.”
Labour leader Sir Keir Starmer said the birth was “wonderful news” as he congratulated the couple on Twitter.
At Prime Minister’s Questions, Mr Starmer added: “Whatever differences we have in this House, as human beings I think we all recognise the anxiety that the Prime Minister and Carrie must have gone through in these past few weeks—unimaginable anxiety—so I really hope that this brings them incredible relief and joy.”
SNP Westminster leader wished “long life and happiness to the new born”.
Chancellor Rishi Sunak said it was “great to hear Downing Street is getting a new resident”.
And the Prime Minister’s father, Stanley Johnson, told the PA news agency he was “absolutely delighted” and “thrilled” by the birth of his grandson.
Acting Liberal Democrat leader Sir Ed Davey said: “Many congratulations to the PM and Carrie Symonds on the birth of their son!”
Foreign leaders, including Australia’s PM Scott Morrison and Japanese premier Shinzo Abe, also sent their wishes.
Mr Abe tweeted: “My dear friend Boris Johnson, warmest congratulations on the birth of a sweet baby boy!”
The Archbishop of Canterbury, Justin Welby, tweeted: “Wishing them every blessing and happiness.”
Mr Johnson and Ms Symonds made history as the first unmarried couple to officially live together in Downing Street when they moved in nine months ago, a few days after he became Prime Minister.
The baby is Ms Symonds’ first child, while Mr Johnson is known to have five others.
Under paternity leave rules, Mr Johnson must take his time off within six weeks of his son’s birth - unless he agrees to share Ms Symonds’ maternity leave.