The Osbournes star and Stelly revealed last week that they had got engaged after dating for months.
Jack has now chided the press for contacting Stelly's family in the hope of securing an exclusive interview.
He tweeted: "Dear Journalists, please refrain from contacting my fiancés (sic) family. Don't be assholes. There is a right way to go about this."
His sister Kelly Osbourne reacted to the engagement by saying that she was "unbelievably proud" of Jack for proposing to Stelly.
Kelly later added that Stelly is Jack's first girlfriend of which she has ever fully approved.
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