The couple said their “healthy baby boy" was born at a London hospital on Wednesday (29 April) morning.
A 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.
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.
What will the new baby be called?
Attention now will be on what Mr Johnson and Ms Symonds will call their newborn child.
Alexander and Winston are also thought to be likely options considered by the couple, but Wilfred was proving so popular with punters that Ladbrokes slashed odds to just 3/1.
William Hill has Wilfred as the 9/2 favourite, and Winston at 8/1, with the bookmaker’s spokesman saying he believes Mr Johnson and Ms Symonds will go with “a seriously posh name”.
According to Oddshecker, which collates the odds offered by various bookmakers and offers a comparison between them, the current best odds for the name of Johnson's new baby are as follows:
- Wilfred – 5/1
- George – 8/1
- Thomas – 8/1
- Arthur - 10/1
- Oliver - 12/1
- Winston - 12/1
- Charlie - 16/1
- Jack - 16/1
- Sebastien - 25/1
- Horatio - 33/1
- Rishi - 100/1
- Vladimir - 250/1
- Brexit - 500/1
Oddschecker spokesperson Callum Wilson said: “Boris Johnson's sleepless nights have just got longer, as the PM's newborn son is about to become Number 10's latest resident.
“Though Wilfred is the bookies' favourite in this interesting market, there are still some questions regarding whether BoJo will elect for a more modern name for his youngster.”
Wilfred - the current bookies' favourite, derives from Germanic roots, and means "he who wants peace".
Perhaps inspired by the chancellor, Rishi is 100/1, followed by Vladimir (250/1) and Brexit (500/1).
Will Johnson take paternity leave?
Mr Johnson had previously said he would take paternity leave in the summer when the baby was due, but because of the ongoing crisis he has been forced to put it off.
His press secretary said: “I do expect the Prime Minister to take a short period of paternity leave later in the year, rather than now.”
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.
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.
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’.