The America's Got Talent judge thanked those who had offered her family support and messages and goodwill following the news and said that her son intends to help others living with the condition.
"Osbournes survive everything. We really do. Jack is doing really, really well," The Sun quotes Sharon as saying.
"He is really a positive guy, a good guy. His whole life is that he gives back. It makes him feel good and that is just the way he runs his life."
Explaining that her son "wants to do as much as he can for MS" alongside his work for Alcoholics Anonymous, Sharon added: "I have to thank you, everyone, for all their good wishes. It's been amazing for Jack, because I really believe that vibes of prayer definitely help."
Jack recently revealed that he has the "most common and least aggressive" form of MS and has said he is optimistic that a cure for the autoimmune condition will be discovered in his lifetime.