Sam Callahan exited the show following a sing-off with Luke Friend. The result means that Boys mentor Louis Walsh has lost his first contestant of the series.
Sam took on 'Iris' by the Goo Goo Dolls in the sing-off, while Luke performed U2's 'I Still Haven't Found What I'm Looking For'.
Walsh chose not to participate in this week's vote as he did not want to choose between his acts.
Nicole Scherzinger opted to send home Callahan ahead of Friend. She threw a pen at Callahan and told him that she was "frustrated" that he left it too late to give a strong vocal performance.
Meanwhile, Gary Barlow explained that Friend is a "unique" and "brilliant act". He pointed out that Callahan's sing-off performance was his strongest of the entire competition, but chose to send him home.
Osbourne said that she too would have sent home the 19-year-old. She also expressed her disappointment that he left it until he was in the sing-off to connect on stage.
Callahan told host Dermot O'Leary: "I've had the most amazing time and I have absolutely no regrets. As far as I'm concerned this is just the beginning of a massive, massive adventure. Thank you guys for being a part of it."
Walsh added: "He's a fantastic role model. He deserves to be successful whatever he does."
Speaking on The Xtra Factor, Walsh said that Callahan will go far as he has an "amazing work ethic".
The latest live results show of the year saw live performances from Miley Cyrus and Barlow, who performed his new solo single 'Let Me Go'.
Meanwhile, the finalists came together for a joint rendition of Take That classic 'Never Forget' at the start of the programme.
The X Factor continues next Saturday (November 23) at 8pm on ITV. One Direction, JLS, Mary J Blige, Olly Murs and Jessie J will all perform on the show next weekend to celebrate its 10th birthday.
The X Factor: Week 6 elimination in pictures: