The former All Black, 28, is over the moon at her arrival.
"To see this beautiful little girl being born was nothing short of amazing," he told the magazine. "You can't explain it in words.
"I just want to do the best for my family and to ensure both she and Amy are always cared for.
"Everything has greater meaning and everything I do is for them," he said.
Before the birth, Kahui joked on Facebook with friends who are also new parents about setting up their offspring.
"Have you thought about a prearranged marriage?" he quipped.
"When I let mini Kaks start dating at 30 I want to know the boy and his parents."
The pair found out only two weeks before their fairytale wedding last April that they were expecting a child.
Meanwhile, broadcaster and writer Jaquie Brown has also given birth to a girl - Ivy Belle, a sister for Leo, 3.
In announcing the birth on Twitter on January 13, she said the little girl had "dark hair, light eyes, smells like sleepless nights and love". She, too, weighed 3.2kg.