The couple spoke to midwifes, who helped deliver their son at UCLH, via Zoom from the study at No 10 on Saturday.
The first two-months of Wilfred’s life have seen a period of great turmoil at Downing Street with his father leading the country’s response to the coronavirus pandemic.
He was also born two days after Mr Johnson returned from St Thomas’ hospital where he spent several nights in intensive care, battling with Covid-19.
The Prime Minister recently said he has been a “pretty hands-on” father to his baby son born during the pandemic.
He told LBC in June that Wilfred is a “wonderful kid” and becoming a father is “an absolutely wonderful time”.
Asked by presenter Nick Ferrari “what’s the best part… cuddling him, changing him, feeding him, reading to him?”, Mr Johnson replied: “All that… it is a very detailed operation and there’s a lot of it, but I’m pretty hands-on.”
It comes after the Prime Minister said, during a visit to a Hertfordshire school, that he had “changed a lot of nappies”, in comments carried by the Daily Mail.
Ms Symonds revealed that she, too, had been bedridden with symptoms of the disease, but had made a full recovery.
The pair had been separated for a period due to the sickness, with Ms Symonds said to have sent letters and baby scans to Mr Johnson to boost his morale while he was in care.
Ms Symonds announced their son’s full name, Wilfred Lawrie Nicholas Johnson, on Instagram a few days after his birth.
She said Nicholas was chosen after the doctors who saved Mr Johnson’s life during his battle with coronavirus.
The 32-year-old also posted a picture of her cradling the newborn, saying she “couldn’t be happier” and that her “heart is full”.
“Introducing Wilfred Lawrie Nicholas Johnson born on 29.04.20 at 9am,” she wrote.
“Wilfred after Boris’ grandfather Lawrie after my grandfather Nicholas after Dr Nick Price and Dr Nick Hart – the two doctors that saved Boris’ life last month.
“Thank you so, so much to the incredible NHS maternity team at UCLH that looked after us so well. I couldn’t be happier. My heart is full.”
Mr Johnson, 55, was present for the birth and said he will take paternity leave later in the year.
The couple have been together since early 2019 and made made history as the first unmarried couple to live in Downing Street after moving in last July.
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.
David Cameron and wife Samantha welcomed daughter Florence in 2010.
The last babies born to prime ministers before Leo and Florence arrived more than 150 years ago.
Wilfred is Ms Symonds’s first child, while Mr Johnson is known to have fathered five others.