"While I was waiting for the final results, I got really, really angry. 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,'" he told Hello! "'Adapt and overcome' is my new motto."
Parents Ozzy and Sharon said they were still coming to terms with the news that their son has the condition.
"I keep thinking, 'What did I do wrong? What did I eat or drink when I was pregnant?'" Sharon told Hello! "I feel like it's somehow my fault."
Ozzy 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."
The Osbourne matriarch delivered an emotional response to news of her son's diagnosis on her CBS show The Talk on Monday.
"Sharon, you have always been an open book with your life, with your family's life, and right now there's something going on with Jack," said co-host Julie Chen as she opened the show.
"Jack will be here on Wednesday to talk about his diagnosis, but he's great," Sharon said. "He's doing really, really good, and I want to thank everyone for all their texts and goodwill and love they've sent to us.
"Thank you to everyone for all their good wishes, it's been amazing for Jack," she continued.
"I really believe that vibes and prayer help, good energy ... What I'm doing right now is not helping because I'm just feeling sorry for myself, and that is no good. So we have to think positively and get on with this show that we love!"
Jack has also reached out to his fans to thank them for their support.
"Thank you all so much for the kind and inspirational words. It means a lot. #adaptandovercome," he tweeted.
His sister Kelly also wrote: "please support my brother @mrjacko in not only his bravery but honesty! i love you so much jack & I'm so proud of you!"
Watch Sharon's message on The Talk below:
For more information about multiple sclerosis, visit www.msnz.org.nz.
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