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The infant, born in London late Saturday, joins big brother Billy, who is 4.
"They are absolutely delighted they have a daughter," the actress's rep, Karon Maskill, tells PEOPLE. "It's a lovely Christmas present for the family."
Bonham Carter, 41, and Burton, 49, have had a busy time of late. Both were nominated for Golden Globe awards for Sweeney Todd – she for best actress, he for best director. In fact, they got that news while at the doctor's office.
"We were talking about inducing, and Tim got a call from his assistant," Bonham Carter told PEOPLE before the birth. "I do look like a globe, so it's kind of funny. I am very round."
She also joked that it was probably hard on the baby while in utero to listen to Mom learning how to sing for her role in the musical. "Maybe the baby's going to come out with his hands on his ears. 'Shut up!' " she laughed.
She added that the anticipation of meeting the new baby was intense. "I just can't wait," she said. "It's hard to imagine we can make anything other than Billy."
The couple revealed the pregnancy exclusively to PEOPLE in August.
Reporting by LISA INGRASSIA
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