The proud mum-of-three wrote on Instagram: "Don't think I have ever felt so complete snuggles with mummy.
"I am absolutely head over heels madly in love.
"With Arabella, I cry everyday with how unbelievably grateful I am for her little life."
Dubbing the little bundle of joy as a 'gift from God', Rebecca added: "Arabella you melt my heart!"
28-year-old Rebecca has two children from a previous relationship, Lillie May and her son, also named Karl.
Her current partner - Arabella's father - prefers to stay out of the limelight, according to Glamour magazine.