The new addition is believed to have been born two weeks ago.
Violet will be little sister to the couple’s eldest child, two-year-old daughter Hazel Grace.
"She's sort of coming around to it," 33-year-old Blunt told E! News back in April of how Hazel was taking the news that there was another baby on the way.
"She sort of dismissed the idea initially and she just responded with, 'Nope.' 'Nope,' flat out! We've bought her every single 'I'm a big sister' book that's out there and she's a bookworm, so she's coming around."
Dting dad John also opened up earlier this year about how fatherhood has changed him.
“I had my daughter [and there was this] existential crack that happens to everybody in a different way — it’s a mirror that you hold up to yourself and who you are and who you want to be,” the Office star told Us Weekly. “I think those are amazing, challenging moments. That you all of a sudden relate to your parents more, you relate to your brothers more, you relate to your friends more.”