Sharing an adorable photo on Instagram, the proud parents gushed over their precious baby boy to their legion of fans.
"Lucius Brunelli," they wrote, revealing his unique name.
"He's here. He's perfect."
Michael clarified the pronunciation of their baby boy's name in the comments, writing: “LOO-SHUS if you’re wondering".
Martha and Michael's famous friends flocked to the comments sections to congratulate the pair.
"Omg what a little angel," Sophie Monk commented.
"Congratulations! He’s beautiful x" model Jesinta Franklin said.
The couple announced the pregnancy in September after Martha's mysterious absence from social media.
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.
Never miss a thing. Sign up to Yahoo Lifestyle’s daily newsletter.
Or if you have a story idea, email us at firstname.lastname@example.org.