Sam Taylor-Wood - the 20-year-old actor`s fiancee - gave birth to a girl, who they have named Wylda Rae, on 07.07.10.
Aaron`s `Kick Ass` co-star Christopher Mintz-Plasse confirmed the news, writing on his twitter account: "Crazier news. AaronJohnson`s baby was born! So exciting!"
This is the first child for the couple who met on the set of John Lennon biopic `Nowhere Boy` last year.
The pair live together in an £11 million north London townhouse, along with 43-year-old Sam`s daughters from a previous marriage, 13-year-old Angelica and five-year-old Jessie.
Aaron has previously insisted he doesn`t care about the 23-year age gap between him and the artist-and-director.
He said: "To be honest, I`ve never really lived life by the rule book. I`ve had a different life to most people. I`ve had to be independent and take on a lot."
Sam also defended the relationship in May, saying: "I-m in love, I-m blissfully content. No one-s getting hurt. We-re in a loving relationship. We-re engaged. Everyone who matters is happy. Exactly which bit of that do I have to defend or apologise for?"