Abbey, who is married to Stoke footballer Peter Crouch, took the crown ahead of newsreader Susanna Reid, soap actress Natalie Gumede and singer Sophie Ellis Bextor, in the show's first all-female final.
"I just can't believe this," said Liverpudlian Abbey. "I'm just so shocked. It's mad."
The model added that her daughter Sophia would be "so happy" that her mum had won.
"She will love this," said the 27-year-old on her glitter ball trophy. "It will go in her room."
Natalie Gumede, who played Kirsty Soames in Coronation Street for 18 months until earlier this year, shed an emotional tear as judge Bruno Tonioli described her final performance as one the best he had ever seen.
In the final round, which the judges scored out of 120, Natalie was awarded 119, Abbey 116 and Susanna 112, before the general public decided who was their Strictly champion.
Earlier in the evening pop star Sophie and her partner Brendan Cole narrowly missed out on making the final three.
"I didn't come here to win," said Sophie, who is a mother-of-three. "I came here to dance."
"You were amazing," said Brendan, consoling her. "Absolutely amazing."