The couple said their “healthy baby boy" was born at a London hospital on Wednesday (29 April) morning and their spokesman said both mother and baby are doing very well.
The spokeswoman said: "The Prime Minister and Ms Symonds are thrilled to announce the birth of a healthy baby boy at a London hospital earlier this morning. Both mother and baby are doing very well."
The news of the birth comes just weeks after after Mr Johnson was discharged from intensive care at St Thomas's Hospital, where he was critically ill with coronavirus.
Ms Symonds also suffered symptoms of the disease but did not require hospital treatment.
Mr Johnson was in hospital for a week before being discharged to recuperate at his country home Chequers. He was only deemed well enough to return to work in Downing Street on Monday.
The baby boy is Ms Symonds' first child. Mr Johnson is known to have at least five children - four in his previous marriage and his new baby with Ms Symonds - although there is speculation he has at least one other child.
Can Prime Ministers take paternity leave?
In the UK, new fathers can take up to two weeks’ statutory paternity leave and eligible employees are paid whichever is lower of £148.68 a week or 90% of their average weekly earnings.
Mr Johnson is entitled to the same paternity leave as every other new father in the country.
The new arrival is the third baby born to a serving prime minister in recent history.
Tony Blair's wife Cherie gave birth to son Leo in May 2000, three years after her husband's first election victory, and David Cameron and wife Samantha welcomed daughter Florence in 2010.
Cameron took his statutory two weeks’ leave, though Blair refused to take paternity leave, instead saying he would temporarily be in ‘holiday mode’.
Will Boris Johnson take paternity leave?
Mr Johnson has previously suggested he would take paternity leave, but it is now not likely he will do so anytime soon, given the current coronavirus crisis.
However, he will reportedly "take paternity leave later in the year" as reported by the London Evening Standard.
Mr Johnson could face a race against time, however, if he is to use his statutory paternity leave as under the law it must be taken 56 days from the date of the birth.
He did not, however, appear at Prime Minister's Questions in the Commons on Wednesday afternoon.
No 10 announced Mr Johnson would not be taking part and his deputy, Dominic Raab, would stand in for him.