Jack Osbourne has thanked fans for their ''kind words'' following the birth of his second daughter.

The 29-year-old star and wife Lisa welcomed baby Andy Rose - a sibling for three-year-old Pearl - into the world on Saturday (13.06.15) and have been toasting their new arrival with non-alcoholic sparkling cider.

Posting a picture of the drink alongside two crystal glasses, Jack - who recently celebrated 12 years being drug and alcohol-free - wrote on Instagram: ''This is how you celebrate when Mum is breastfeeding and Dad is sober. Thank you all for the kind words. #newbaby (sic)''

Meanwhile, Lisa has been tucking into Milkmakers' lactation cookies - which contain ingredients to help boost a nursing mother's milk supply - and is enjoying the chocolate chip and oatmeal variety so much, she is worried about what will happen.

Posting a picture of the bag of cookies, she wrote: ''What happens if I eat the whole bag? #icantstop #theyresodelicious (sic)''

The couple announced they were set to add to their brood by sharing a photo of Lisa's blossoming baby bump on Jack's Instagram profile in February.

Lisa, 28, also revealed the news on her blog, Raddest Mom, and shared Pearl's excitement at becoming a big sister.

She said: ''Pearl is very happy to become a big sister. She diligently reads her 'I'm a big sister' books every night & recites to me her plans of bathing, feeding, singing to, and holding the baby.''