Their new arrival will be known as "Wilfred Lawrie Nicholas Johnson," Symonds wrote on her Instagram page Saturday.
Symonds, 32, an environmental activist and former official in Johnson's ruling Conservative Party said the name Wilfred came from the prime minister's grandfather and Lawrie from her grandfather.
Nicholas was inspired by the names of two doctors, both called Nick, who treated Johnson when he was sick in hospital with COVID-19 last month.
"I couldn't be happier. My heart is full," Symonds wrote alongside a picture of her cradling her new son.
Wilfred Johnson was born healthy at University College Hospital in London Wednesday morning, she said, adding that the couple wanted to thank their "fantastic" maternity team.
The prime minister, 55, recently recovered from COVID-19 after spending days in the intensive care unit of a London hospital. He was discharged on April 12 and thanked staff with Britain's National Health Service "for saving my life."
Symonds, said she also had COVID-19 symptoms while pregnant but was not tested.
Johnson, returned to work this week as the United Kingdom recorded more than 27,000 deaths from COVID-19 — giving it one of the highest death tolls in Europe. Some have criticized his government's response to the crisis.
For years Johnson's private life has been the subject of some speculation, fueled in part by his repeated refusal to confirm how many children he has.
He has been married twice before and fathered four children with his second wife Marina Wheeler, a prominent barrister. The couple separated after 25 years in September 2018 and later divorced.
In 2013, when Johnson was Mayor of London, appeal court judges ruled that the public had the right to know whether he had an extramarital affair with a woman who gave birth to his daughter.
This is his first child with Symonds, and their wedding would be the first for a sitting prime minister in some 250 years.