Model Lisa, 27, announced the news on her second pregnancy via her blog on Monday, revealing that she is now in her second trimester.
"Jack and I are super excited to share with you all that we are expecting our second baby," she wrote underneath a picture of herself with her husband and daughter.
"I am in my second trimester, feeling great & trying not to eat everything in sight," she added in the blog, titled The Raddest Mom.
"We feel so blessed that our family is growing & Pearl will have a little brother or sister to play with. It's crazy to think we will soon be a family of four!"
Leaving it to his wife to make the happy announcement, Jack retweeted a link to Lisa's blog with the words, "Pregnancy announcement!"
Jack, 27, and Lisa married in Hawaii in October 2012, six months after the arrival of their firstborn.
The new baby will be the second grandchild for Ozzy and Sharon Osbourne, who told People in April that her son Jack "wants about five kids and Lisa comes from a big family too. They both want to have a whole brood."
The famous family have plenty to celebrate at the moment; Kelly Osbourne recently announced that she was engaged to Matthew Mosshart.
Last week the TV star, 28, praised her younger brother for his ability to cope following his diagnosis a year ago with multiple sclerosis.
"He's amazing. He's unstoppable," she told People. "It's like it's not even there… He always reminds me that it's not just him that we're fighting this race for. It's the 2.1 million people living with it as well."