The pregnant TOWIE star, who is the sister of co-star Sam, is said to be due this summer and she and Greg are "over the moon".
Billie, 23, and 28-year-old Greg apparently told their family their exciting news at Christmas and can't wait to become parents for the first time.
A source told The Sun: "Billie and Greg are over the moon. They've been a couple for two years now and love each other to bits."
Earlier this week, Billie attended Sam's Disney-themed New Year/ birthday party as Tinker Bell and she looked glowing in a green leotard.
The star is said to have stuck to soft drinks all night due to her pregnancy but still looked trim in her costume.
Billie has been dating Greg for two years, however she has kept their relationship away from the TOWIE cameras at his request.
Although Billie's rep wouldn't confirm their baby news, he said he had no comment to make.
Since getting together with Greg, Billie - who lives with her man in Brentwood - has made no secret of the fact that she wanted to have children with him.
An insider tells Reveal: "She's always talking about how much she'd love to become a mum."
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