The X Factor finalist, 28, announced the happy news via Twitter.
After updating her fans during her "slow labour", she finally had good news to share on Saturday (25 October).
She said: "I don't want to sleep, I just want to look at her... Thank you for all the love and support. Will update you all tomorrow my angel is here xx."
The singer also told her fans that she can't take her eyes off her newborn daughter.
She later added: "She is so perfect. My Arabella is like a beautiful little doll xxx.
"Can't put her down she is ruined already such a happy mum xxx."
It is Rebecca's first child with her boyfriend, who she has been with for over a year, but refuses to name.
I don't want to sleep I just want to look at her ... thank you for all the love and support will update you all tommorow my angel is here xx— Rebecca Ferguson (@RebeccaFMusic) October 25, 2014
She already has two children, Lillie May, nine, and Karl, seven, from a previous relationship.
Rebecca revealed she was pregnant in April after collapsing during a performance on ITV1's Loose Women.
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