Rebekah played paramedic Nina Farr on the BBC soap between 2004 and 2006, appearing in more than 100 episodes.
Prior to her role on 'Casualty' she had also appeared in 'The Bill' on ITV.
Her agent Belfield and Ward tweeted the news: "Darling Rebekah Gibbs, a true inspiration and dazzling light, never to be forgotten."
Darling Rebekah Gibbs - a true inspiration and dazzling light - never to be forgotten. pic.twitter.com/4VAsZcS3gW— Belfield & Ward (@BelfieldWard) November 11, 2014
She left 'Casualty' to start a family and had a daughter, Gigi, in 2008.
Just weeks before giving birth she discovered a lump in her breast and was later told that she had a particularly aggressive cancer.
She wrote about her experience in a weekly column for the Daily Mirror, saying the exact moment she found the lump was one that would stay with her forever.
"I close my eyes, and I am right back there, in front of the TV, feeling petrified as I desperately run my finger above my baby bump and under my breast, willing the lump to disappear," she wrote.
"That crushing fear has stayed with me. It's with me every day."
The actress was given the five year all-clear from cancer in April, and said at the time that she was 'really content' to have reached the milestone.
However in August she had a seizure and was diagnosed with two brain tumours.
Speaking in April she said: "I was in Devon with my family when I had a huge seizure.
"Within an hour I was in A&E. I was quickly diagnosed with two brain tumours, plus one in the neck and a lesion on my lung."
'Coronation Street' star Hayley Tamaddon' and actor James Redmond, who starred alongside the actress in 'Casualty', have taken to Twitter to pay their respects.
So sad to hear lovely Rebekah Gibbs has passed away.She lit up every room with her smile & positivity.R.I.P. pic.twitter.com/JHzyUSMWdV— James Redmond (@James_Redmond_1) November 12, 2014
Rebekah is survived by her husband Ashley Pitman and her daughter Gigi, aged six.