In an interview with Hello! magazine, Osbourne, 60, said:
As soon as I found out I had the breast cancer gene, I thought: 'The odds are not in my favour'.
I've had cancer before and I didn't want to live under that cloud: I decided to just take everything off, and had a double mastectomy.
More top news
The Which? annual survey saw British Airways languishing near the bottom for passenger satisfaction for both short and long-haul.
The Orkney Islands took second place, followed by Rutland and Wychavon while last year's winner Winchester falls to fifth place.
The prime minister reached a compromise deal within Tory ranks in a bid to prevent a revolt over plans to write the Brexit date in law.