The duo shared the news, and the newborn's name in a post on Instagram, writing: "He’s finally here. Just wanted to say hi with our newest addition to the family Shackleton Stoker Daluz.
"Born at 7:54 am on the 18th of October. What a joy to have him safe and sound in our arms. Thanks for hanging with us through the journey."
The post also featured the duo, Shackleton, and their first child Violet in a video where the parents explain the traumatic birth.
"I decided I wanted to have a natural birth… that didn’t happen!" Joss said. "He was 9lb and 2oz, a slight bit bigger than the doctors had [expected].
"I had labour for 30 hours – that’s a long time! And then it all went a bit tits up – actually I think it was 32 hours in the end. So he was born at 7.54am on the 18th and it was because my uterus split.
"Basically he was a bit big... I’m in the one percent, apparently! Anyway, so the doctors and nurses at Vanderbilt saved my life and saved his life, they are amazing and we love you guys at Vanderbilt, thank you so much."
Cody admitted that there was about 20 minutes where he genuinely thought he was going to lose Joss and the baby, and wondered if he was going to have raise Violet as a single father.
When she announced that she was pregnant earlier this year, Joss revealed that she had lost a baby a year ago.
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