A now-deleted message on the 32-year-old's verified account had said she "died unexpectedly on Wednesday night."
But a video subsequently posted on her Twitter page showed her dismissing the reports - which had been covered by a series of news outlets, including The Independent.
"Hi everyone - I just want to kindly ask, please stop spreading the news that I'm dead because obviously I'm not," she said.
"I've been through hell today because someone used my Twitter account to write that stupid status about me.
"This person can't accept the fact that I'm happy, that I overcame all my problems and that I'm finally living my life happy.
"I'm on holiday, I'm in Arabia, and I'm not dead."
A statement posted to Ms Shelton’s Twitter account earlier today, read: “We’re sorry to inform everyone of the sad news that our wonderful and lovely Rebekah died unexpectedly on Wednesday night.
“We ask that you respect the family’s privacy at this time.”
Many people responded to the original tweet with messages of condolences, including the official Big Brother account.
Ms Shelton appeared on Big Brother in 2009 as Rodrigo Lopes, finishing in fifth place.
She underwent gender reassignment surgery in 2014.
She previously spoke to OK! Magazine about her transition, saying she had to “fight for acceptance”.
“I was not born wanting to be a transsexual, or a boy, or a straight boy, or a girl,” she said in the 2015 interview.
“I think my appearance on the show [Big Brother] helped me to get to know myself better.
“It gave me the acceptance I had been looking for my entire life – I started dressing like the girls, and I felt like I was getting to know myself better with every new piece of clothing.”