The 29-year-old actress and French journalist Romain Dauriac, 31, welcomed their daughter - who they have named Rose - to the world on Thursday. She is the couple's first child.
Their representative said Scarlett and Rose are both doing well, but they are seeking privacy because they don't want their baby to grow up in the spotlight.
The couple, who became engaged last summer, sparked rumours they were expecting a child together in March this year, just three months after Scarlett revealed that she was keen to start a family.
She said at the time: "I would like to have my own family, that would be nice.
"They say it's never the right time and I am sure that's true, but I think you have to plan it like anything else. At some point it is something I look forward to."
Scarlett has said she doesn't want to 'rush' tying the knot as 'being engaged is an exciting time to enjoy and to really savour.'
When she does, it will be Scarlett's second wedding as she was previously married to Ryan Reynolds from 2008 until 2011.
While she was pregnant, Marvel Studios President of Production Kevin Feige, who worked with Scarlett on the Avengers: Age of Ulton movie, discussed how her pregnancy affected filming.
He said: "Well my first reaction was I was very happy for her and very excited for her.
"My second reaction was we've got to move some pieces on the chess board around schedule-wise. But we didn't change the script at all, which is sort of the most important things for us in terms of the storyline."