The message is accompanied by a photo of the baby clutching at her mother's thumb, while Richie's hand cradles both of theirs.
Gemma and hubby Richie announced their pregnancy back in July.
In the same social media style, she posted a photo of a tiny pair of adidas running shoes between a men's and women's pair saying: "Rich and I are very excited to announce that we are expecting our first baby later this year."
Gemma, a former Black Sticks star, and Richie were married in January 2017 and the child is their first.
Richie's father, Donald McCaw, told the Herald they were thrilled at the birth of their new granddaughter. He said they had met her earlier in the week.
The announcement received hundreds of likes and dozens of comments within minutes of being posted.
We are proud to announce the arrival of Charlotte Rose McCaw to the world. Both Mum and baby are doing great.
Posted by Richie McCaw on Wednesday, 12 December 2018
The Hits host Toni Street said she was thrilled for the McCaws.
"Awww yay team McCaw! Congrats Gem & Rich, Matt and I are thrilled for you guys, what a beautiful name can't wait to meet her," she commented on Instagram.
Paralympian Sophie Pascoe sent her well wishes, saying: "Congratulations to you both!".
Richie's former teammate Keven Mealamu commented three heart emojis.
Fatima Savea, wife of former All Black Julian Savea, welcomed Gemma to "mama hood". "Congratulations family! Welcome to mama hood."
