Jack's rep confirmed on Friday that he had recently proposed to Stelly after dating for several months.
Kelly joked on Twitter that Jack's impending marriage means that he has finally become a man.
She tweeted: "well i guess you're not my little brother anymore i'm so unbeliveably proud of the man you have become! im so happy for you & lisa! (sic)"
Kelly was engaged to boyfriend Luke Worrall in 2008, but they broke up amid rumours that Worrall had been unfaithful.
Earlier this month, Kelly credited Jack with helping their dad Ozzy Osbourne get sober.
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