Rachel Zoe has revealed the name of her newborn son.

The 42-year-old former The Rachel Zoe Project star and celebrity stylist welcomed her second baby boy with husband Rodger Berman into the world on Sunday and has announced the couple has named him Kaius Jagger Berman.

"As loyal readers of The Zoe Report, I wanted you to be the first to see a picture of the beautiful new addition to our family, Kaius Jagger Berman, aka 'Kai,'" Zoe wrote on her official website, The Zoe Report, on Monday.

Kaius has joined the couple's first child Skyler, who was born in March 2011.

"Rodger, Skyler and I are madly in love and will be happily hibernating for the next couple of weeks. Thank you for all of your kind words, as they mean so much to us. Wishing you and your family a wonderful holiday and Happy New Year! Love, Rachel Zoe," she added.

Along with the message, Zoe posted a black and white photo of herself, Berman and Kaius. She was holding the baby while sitting in her hospital bed.

Kaius was born weighing seven pounds and 12 ounces. When Zoe announced she had given birth to boy, she said he was "beautiful and healthy."

Zoe and Berman wed in 1996 and have been married for about 14 years.

In August, Zoe had confirmed The Rachel Zoe Project is unlikely to return to Bravo for a sixth season.