The Paralympic medal winner and husband Rob Samson shared an image on Instagram.
"It's been the best few weeks already with our baby boy, We are just so in love!", she said.
Dame Sophie has represented New Zealand at four Paralympic Games and two Commonwealth Games, winning a total of 11 Paralympic gold medals.
She is New Zealand's most decorated paralympian.
In 2022 she was made a Dame Companion of the New Zealand Order of Merit for services to swimming in the New Year's honours list.
She made her international debut when she was only 13, and at 15 won three golds and one silver at the 2008 Beijing ParalympicGames.
Dame Sophie has also been named disabled sportsperson of the year on six occasions at the Halberg Awards and was named para athlete of the decade in 2020.