Northern Ireland's politicians were among those sending well-wishes to Prime Minister Boris Johnson and fiancee Carrie Symonds on the birth of their son.
A spokeswoman for the Prime Minister and his partner said that both mother and baby were "doing very well" following the birth in a London hospital yesterday.
It is understood Mr Johnson was present throughout the birth. The 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 PM and Ms Symonds would like to thank the fantastic NHS maternity team."
First Minister Arlene Foster tweeted: "Wonderful news of the birth of a baby boy! Many congratulations to the PM @BorisJohnson and @carriesymonds. More sleepless nights ahead!"
UUP leader Steve Aiken also took to Twitter. He said: "Congratulations to Carrie & Boris and we wish them, and their son, all the best (and to pass on our wishes to all other newborns and parents as well)."
Secretary of State Brandon Lewis also tweeted his congratulations.
Mr Johnson (55) and Ms Symonds (32) announced in February that they were expecting a baby in "early summer", and said they had become engaged at the end of last year.
The news of the birth comes just weeks after the PM was discharged from intensive care where he had been battling coronavirus.
Ms Symonds also suffered symptoms of the disease. She returned to Downing Street after joining Mr Johnson as he convalesced at Chequers, but it is not yet known which hospital she gave birth in. Mr Johnson has previously suggested he intends to take paternity leave, although it is not known if this remains the case given the current crisis.
He did not appear at Prime Minister's Questions in the Commons yesterday.
At the daily Downing Street press conference Foreign Secretary Dominic Raab said he had spoken to Mr Johnson and that the Prime Minister's fiancee and their newborn son were "doing really well".
Earlier Labour leader Sir Keir Starmer said the birth was "wonderful news" as he congratulated the couple on Twitter.
Acting Liberal Democrat leader Sir Ed Davey said: "Many congratulations to the PM and Carrie Symonds on the birth of their son."
Chancellor Rishi Sunak said it was "great to hear Downing Street is getting a new resident".
And the PM's father, Stanley Johnson, told the PA news agency he was "absolutely delighted" and "thrilled" by the birth of his grandson.
Foreign leaders, including Australia's PM Scott Morrison and Japanese premier Shinzo Abe, also sent their wishes.
The Archbishop of Canterbury, Justin Welby, tweeted: "Wishing them every blessing and happiness."
Mr Johnson and Ms Symonds made history as the first unmarried couple to officially live together in Downing Street when they moved in last year. 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, and David Cameron and wife Samantha welcomed daughter Florence in 2010.
The last babies born to PMs before Leo and Florence arrived more than 150 years ago.
The baby is Ms Symonds' first child, while Mr Johnson is known to have fathered five other children.