"My beautiful wife, and son Milo Green," he captioned the post.
"On Wednesday evening during a power cut Matty gave birth naturally in our lounge. She was incredible, using breathing techniques to remain calm and strong throughout. I even got to deliver the little guy. Tell ya what, they are slippery little octopuses when they come out. Everyone is happy and healthy and filled with love."
The couple recently shared photos of their son's nursery on Instagram, captioning the image: "See you soon little man, we're ready and waiting for you! #39weeks"
The photo revealed a cosy armchair covered with a sheepskin, a chest of drawers with books and toys and two sketches of rabbits hung on duck-egg blue walls.
In April, the Instagram-savvy duo announced they were "so bloody excited" to be expecting a boy, and told Woman's Day he will be a "free-range baby".
"We really want our kids to grow up surrounded by nature and, as a family, living off the land as best we can."
The Greens, who met on the first season of New Zealand's edition of The Bachelor in 2015, have been together for four years. The couple recently bought their first home together in Warkworth and run several businesses.
In February they got married on Waiheke Island in a small ceremony where Matilda also took the opportunity to announce her pregnancy to family and friends.