She wrote on her blog, Raddest Mom, "I have been dreading this announcement ... I needed some time before being able to say it."
"Jack and I lost our baby boy last week. Having a late term miscarriage is by far the hardest thing either of us have ever had to go through. We appreciate all of your prayers and ask for privacy and respect during this time."
The couple, who are parents to 16-month old daughter Pearl, are trying to stay positive.
"It's important to stay hopeful and optimistic through life's toughest moments, we never know why things like this happen. All we can do is trust in God and know he has a plan for our lives."
The couple announced their pregnancy on August 5.
Doctors describe a late miscarriage as one that happens after 12 weeks and before 20 weeks of pregnancy. Baby Center says, Late miscarriages are more likely than early miscarriages to be linked to a health problem with the mom-to-be. Of all miscarriages, about one in 100 happens later in pregnancy.
Osbourne, the son of Ozzy and Sharon Osbourne, is currently training for "Dancing With the Stars."