Jessica Alba and Cash Warren are ''over the moon'' by the arrival of their baby boy.

The couple were thrilled to welcome their son Hayes into the world on New Year's Eve and are so happy with their ''little miracle''.

A source said: ''Jessica and Cash are over the moon and in love with their baby boy, Hayes. Jessica had a smooth delivery on New Year's and was able to go home quickly, which she was very happy about. She keeps saying that 'third time's a charm' and how excited everyone is to have a boy in the family. Cash was rooting for a boy, and they are happy about their little miracle ...

''Jessica thinks that the process has been much easier so far because she has been a mom for years now. The girls are really excited to have a brother and already obsessed with him. Hayes has even had many visitors come to the house already, and everyone thinks he looks a lot like Cash.''

Jessica has been recovering at home since the birth but can't wait to head back to work later in the year.

The insider added to E! News: ''Jessica has been recovering. Cash has been very helpful with the basic newborn needs like changing and waking up during the night. Jessica plans to ease back into work later on this year, and will still be heavily involved in Honest Company.''

Meanwhile, Jessica previously revealed that her youngest daughter Haven couldn't wait to have a baby brother.

Speaking before the birth, Jessica - who also has Honor, nine - said: ''My six year old, she was worried about being a middle child, but she gets to be a big sister and a little sister. So, she's stoked about that - and she doesn't have to compete with another girl ... For me, the girls love their dad. I wanted someone to love me more. When he comes home, they're like, 'Daddy!' It's like a party. When I come home, they're like, 'Oh, hey Mom.' I'm like, 'I do everything for you! I cook, I do all the things!'''