Posting a video on Instagram, the stars announced they were expecting a child.
While the pair said it had been an "exciting and wonderful" time, Martha revealed she had been diagnosed with hyperemesis gravidarum.
"It's severe chronic nausea and vomiting with no relief, 24/7," Martha said. "I literally didn't get out of bed for two months."
The couple also revealed Martha lost 10kgs in five weeks as a result of the condition and had been in and out of emergency and hospital.
She said she now had some medication which was "life-changing" and helped her feel "human" again.
Michael added it had been too early to announce the news to fans and thanked those who reached out with their concerns.
"Hopefully now you can relax," he added.
He said in the comments on the video they did not know the gender but had it written down in an envelope.
Martha, who met her fiancé Michael on the reality TV show in 2018, had not posted on Instagram since July, while Michael last posted on August 9.
Friends and fans shared messages of congratulations on their Instagram post announcing the news.
"Sooo excited for you both," one said.
"This is so beautiful, I'm glad you are feeling better," another commented.
"I had severe HG also so I'm feeling for you! It's absolutely horrible. Sending you love," a third added.
Their baby news comes after the pair got engaged last year.
The pair took to their Instagram accounts to upload an adorable selfie, with the caption simply saying: “Mrs B”.
The photo showed Martha’s eye-popping diamond engagement ring from Armans Jewellery, which consisted of a single, stunning, emerald-cut diamond.
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