The 42-year-old BBC Radio 1 breakfast show presenter and former Rock FM DJ, said the diagnosis was confirmed at the beginning of this month and she is set to have surgery to remove a tumour on Monday.
She made the announcement in a social media post where she was smiling, wearing a hospital gown and threw a thumbs up sign.
Roberts said “so far the outlook is positive and I feel so lucky that I can be treated” but she needs to find out if the cancer has spread.
She went on: “It’s just the start of my journey but I’m going to give it everything I’ve got.”
Roberts, from Southport, Merseyside, first found fame in Channel 4’s Big Brother series in 2002 where one of her housemates was Jade Goody, who died in 2009 after being diagnosed with cervical cancer.
She urged everyone to get checked out if they have any concerns as she recalled how her own illness was discovered.
Roberts wrote: “For a while now I’ve been struggling with my digestion.
“Thanks to a conversation I had with my Dad a few years back I went to my GP for a check up. I’ll be honest, I was embarrassed but I also knew that it could be something serious.
“So I went just in case. I didn’t think anything of it at first and just assumed it might be food sensitivity.
“After a few phone calls I was sent for some examinations and checks. I was then diagnosed with bowel cancer. This was at the start of the month.
“It’s all happened so quickly and I’m so sorry to post something like this on here but I hope it helps anyone who might be worrying, or suffering in silence.”
She added: “The sooner you’re able to see your GP or talk to someone the sooner you can get help.
“If I hadn’t I might not be so lucky. As I’ve learned over the last few weeks, there’s no ‘normal’ with cancer.
“Sadly it can affect anyone, at any age, anytime. It doesn’t discriminate. Early detection can save your life.”
Roberts joined the BBC in 2012 as part of the Radio 1 Xtra team, before moving to Radio 1 in 2015 to host the Early Breakfast Show.
She took over the Weekend Breakfast programme earlier this year.
Roberts also appeared on ITV’s I’m A Celebrity in 2019.
Her post drew messages of support from friends and colleagues.
Radio 1 tweeted: “Everyone at Radio 1 – along with all our listeners – is wishing you a speedy recovery and we can’t wait to welcome you back on air soon.”
Radio and television presenter Clara Amfo posted a message which said: “Love you so much.”
DJ Scott Mills wrote: “We all love you Adele. Its amazing you posted this. You’re awesome and you’ve GOT this.”