The TV and music star family said Jack was diagnosed from tests taken when he lost 60% vision in his right eye earlier this year.
Jack Osbourne, 26, told Hello! that after first feeling angry and upset he has now taken an attitude of “adapt and overcome”.
MS is an incurable neurological condition that damages the nerves and affects the transfer of messages around the body.
MS affects the brain and the nervous system and destroys myelin sheath layers between the nerves in the brain and spinal cord which stops impulses being carried around the body.
It can cause blindness, slurred speech, muscle weakness and a loss of coordination.
There is no known cause or cure for MS, which is three times more common in men than in women.
Between 2 and 5% of cases are discovered in children under 16.
Jack Osbourne said he had chosen to speak out in order to raise awareness of the condition. He added that the support of his fiancée Lisa Stelly was helping him to stay positive.
MS can have a wide range of symptoms, including tiredness, temporary blindness, loss of co-ordination and speech difficulties.
It is unpredictable and affects everyone differently. One in five sufferers has a benign form with mild attacks and no permanent disability, while another 15% have a progressive disease that steadily worsens.
Jack Osbourne was diagnosed with the condition three weeks after the birth of daughter Pearl, now two months old.
“The timing was so bad,” he said.
“I’d just had a baby, work was going great – I kept thinking: <<Why now?>>”
Ozzy and Sharon Osbourne said they were still trying to come to terms with their son’s condition.
Former X Factor judge Sharon Osbourne said she had been asking herself if she was to blame.
“I kept thinking: <<What did I do wrong, what did I eat or drink when I was pregnant?>> I feel like it’s somehow my fault.”
Former Black Sabbath star Ozzy Osbourne said: “If it was me, you’d think: <<Ozzy had a reputation and it caught up with him>>, but Jack is such a good guy.”
Jack Osbourne – known as an extreme sports enthusiast – will use a combination of daily drug treatments, holistic therapies and lifestyle changes.
The family was the subject of a worldwide hit reality TV show, The Osbournes, which originally aired on MTV between 2002 and 2005.
The programme, also featuring the Osbournes’ daughter Kelly, won an Emmy award in 2002.
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