Jack Osbourne and LIsa Stelly
10/06/2012 at 06:10 PM EDT
While he did his best to throw off inquiring minds, Tweeting a wedding denial
Friday, Jack Osbourne can't hide it any longer: He married Lisa Stelly on Sunday, his rep confirms to PEOPLE.
The couple exchanged vows in front of 48 close friends and family members, including Osbourne's parents Ozzy and Sharon Osbourne, on the Big Island of Hawaii, according to Hello! magazine
. His sister Kelly Osbourne
was a bridesmaid in the ceremony.
The 26-year-old son of rocker Ozzy, 63, and talk-show host Sharon, who turns 60 Tuesday
, was diagnosed with multiple sclerosis in May
, and told PEOPLE at the time that his wedding would be in "fall sometime ... small and intimate, outside of L.A. somewhere."
The couple welcomed daughter Pearl