The Queen has sent a private message of good wishes to Boris Johnson and Carrie Symonds to congratulate them on the birth of their son, Buckingham Palace said.
The monarch and the PM will speak on the telephone later on Wednesday during their weekly audience.
The call is still scheduled to go ahead despite being due to take place just hours after the arrival of Mr Johnson’s newborn.
Downing Street said the PM, who is currently grappling with the coronavirus crisis, would take a short period of paternity leave later this year.
Mr Johnson’s audiences with the 94-year-old Queen, who is staying at Windsor Castle, have been taking place by telephone during lockdown.
But the weekly calls between Number 10 and the head of state were put on hold while Mr Johnson was in intensive care, and Foreign Secretary Dominic Raab – who deputised for the PM – was not asked to step in to brief the Queen on his behalf.
The Queen sent a message to Mr Johnson’s fiancee Ms Symonds and his family while he was being treated in hospital, wishing him a “full and speedy recovery”.
Mr Johnson is the 14th prime minister of the Queen’s reign.