Carrie Symonds and Boris Johnson have named their baby son Wilfred Lawrie Nicholas Johnson – with the name Nicholas chosen in a nod to the two doctors who saved the prime minister's life.
Announcing the news on Instagram, Ms Symonds said the baby was named after the prime minister's grandfather, Wilfred, and her grandfather, Lawrie.
She said he was also named after the two doctors, Dr Nick Price and Professor Nick Hart, who saved Mr Johnson's life when he was in intensive care with coronavirus last month.
Ms Symonds praised midwives and staff at London's University College Hospital (UCLH), adding: "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."
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The picture shows Ms Symonds, 32, cradling the newborn, who can be seen with a full head of hair.
The baby was born at 9am on Wednesday, she said.
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A spokeswoman for the couple said they were "thrilled" and that both mother and baby were "doing very well" following the birth.
It is understood Mr Johnson was present throughout the birth, with Downing Street releasing a photograph of him beaming on his return to Number 10 following the arrival of his son.
The birth came just weeks after Mr Johnson was discharged from intensive care and a few days after he returned to work on Monday.
Ms Symonds also suffered symptoms of coronavirus.
Last month, after spending seven nights in St Thomas' Hospital in London, Mr Johnson praised the "exemplary" care he received from doctors and nurses during his treatment for COVID-19, saying: "I want to pay my own thanks to the utterly brilliant doctors, leaders in their fields, men and women but several of them for some reason called Nick, who took some crucial decisions a few days ago for which I will be grateful for the rest of my life."
In a joint statement, Dr Price, who is director of infection and consultant in infectious diseases, and Prof Hart, director of respiratory and critical care medicine at Guy's and St Thomas' NHS Trust, said: "Our warm congratulations go to the prime minister and Carrie Symonds on the happy arrival of their beautiful son Wilfred.
"We are honoured and humbled to have been recognised in this way, and we give our thanks to the incredible team of professionals who we work with at Guy's at St Thomas' and who ensure every patient receives the best care.
"We wish the new family every health and happiness."
Mr Johnson also singled out nurses Jenny McGee and Luis Pitarma after his release, but did not use their second names.
Hailing the work of the NHS staff, after admitting things could have gone "either way", the prime minister said: "I can't thank them enough."
Ms Symonds and Mr Johnson announced at the end of February they were expecting a baby in "early summer" and they became engaged at the end of last year.