The couple made the announcement via the first-time father’s Twitter account, tweeting “Wanted to let the news out directly. Emily and I are so incredibly happy to welcome our daughter Hazel in the world today! Happy bday!”
It has been publicised that the couple, who were married in 2010 in Italy, have been planning for children and want a big family.
“We want to have children; I just don’t know when yet,” Blunt said at the time of their marriage.
“I’m just not sure about the timing of all of that. We’re both from big families so I think it’s something we want.”
Blunt, 30, whose breakthrough role was the catty English assistant in The Devil Wears Prada, was last spotted just a few days ago in Hollywood on casual day out with John, 34, star of TV sitcom The Office.
Blunt continued working throughout her pregnancy, filming roles that do not lend themselves to a woman expecting.
Alongside Tom Cruise, she has been filming science-fiction film Edge of Tomorrow, playing a Special Forces soldier fighting a hostile alien race.
When spotted filming Disney’s Into the Woods, a cinematic adaptation of the Broadway musical, her costume reportedly disguised her pregnancy.
Both films are expected to be released next year.