MS is an incurable condition that affects the brain and central nervous system. New research published in the journal Multiple Sclerosis says that one in 20 adults will experience their first MS symptoms during childhood.
Osbourne, 26, is the son of ex-Black Sabbath frontman Ozzy and TV host Sharon. His family was the subject of a hit reality TV show, The Osbournes.
Osbourne's fiancee Lisa Stelly gave birth to daughter Pearl Clementine just two weeks ago.
He and his family revealed the news of his MS in an interview with Hello! magazine.
"While I was waiting for the final results, I got really, really angry," he said, according to the UK Press Association.
"Then I got really sad for about two days, and after that I realized, being angry and upset is not going to do anything at this point — if anything it's only going to make it worse. 'Adapt and overcome' is my new motto."
"I've got a family and that's what's supposed to be the most important thing," he told People magazine.
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Osbourne was tested for the disease after losing 60 percent of the vision in his right eye earlier this year.
MS can have a range of symptoms, including muscle weakness, visual problems, loss of co-ordination and speech difficulties.
Osbourne, who is an extreme sports fan, will treat his MS with a combination of daily drug treatments, holistic therapies and lifestyle changes, including avoiding stress.
Sharon told Hello! that she wondered whether she was to blame for her son's condition.
"I keep thinking: 'What did I do wrong? What did I eat or drink when I was pregnant?' I feel like it's somehow my fault," she said.
Ozzy said in the interview: "If it was me, you'd think: 'Ozzy had a reputation and it caught up with him', but Jack is such a good guy."