Both mother and baby are doing very well, their 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,” their spokesman said on Wednesday.
“The PM and Ms Symonds would like to thank the fantastic NHS maternity team.”
The couple announced at the end of February that Ms Symonds was pregnant and they had got engaged.
Health Secretary Matt Hancock posted on Twitter: “So thrilled for Boris and Carrie. Wonderful to have a moment of unalloyed joy!”
The Leader of the Opposition, Labour’s Keir Starmer, was quick to offer his congratulations, tweeting: “Wonderful news. Many congratulations to Boris Johnson and Carrie Symonds.”
It comes after it was unclear for 24 hours whether Mr Johnson would be attending the weekly session of prime minister’s questions – despite returning to No 10 to resume his responsibilities three days ago.
Dominic Raab, the first secretary of state, will step in for the PM and Sir Keir Starmer, the new Labour leader, will also attend the session.
More to follow.