The 28-year-old took to Twitter to break the news on Saturday evening, after previously complaining of 'slow labour' on Friday afternoon.
But it was obviously totally worth it for Rebecca, who gushed: "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 [sic].
"She is so perfect. My Arabella is like a beautiful little doll xxx [sic]."
Taking to Twitter again this morning, Rebecca showed that the excitement still hadn't worn off, writing: "Can't put her down she is ruined already. Such a happy mum xxx [sic]."
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Rebecca is already mum to nine-year-old daughter Lillie May and son Karl, seven, from a previous relationship.
Arabella is her first child with her current boyfriend, who she has been with for over a year. The singer has chosen not to talk publicly about her relationship, but it is believed she's known him since before appearing on The X Factor in 2010.
The singer found out she was expecting her third child in April this year, after collapsing at a gig. But it took two pregnancy tests before the news was confirmed.
She told the Daily Mail in June: "I was like 'How strange!' I've got all of the pregnancy symptoms but after the show I ended up spending two days resting in bed.
"I kept saying to everyone, I've got pregnancy symptoms so it's really weird and then a couple of days later I took another test and it was positive!"
**Congratulations, Rebecca! **