The 36-year-old Aviator actress gave birth in a Los Angeles hospital on Monday, however the sex of her babies is yet to be confirmed.
According to the Daily Mirror a source has said, "Zoe and Marco are delighted, Zoe has been ready to drop for some time and they are both ecstatic to be meeting the twins.
"This a dream come true for both of them, they are absolutely delighted," the source added. "They have been looking forward this day for the last nine months. Both want a big family so this is the start."
Zoe announced her pregnancy back in July (although Britney Spears did totally give it away beforehand) and has made several red carpet appearances since, showing off her beautiful bigger-by-the-day baby bump.
Most recently she attended the premiere of The Book of Life in mid-October with her husband at LA's Nokia Theatre.
As for Brit giving the game away? In a US TV interview she was asked about collaborating with Zoe again on the big screen and she said, "Who knows? That's a very good idea. But she's pregnant with twins right now. So I'm sure she's got a huge future ahead of her."
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