"It's been a long week for Dame Valerie and Gabriel," Cowan said. "They thank everyone for their love and support this week and the Auckland Hospital Neonatal Intensive Care Unit for all their hard work and amazing care.
"Kepaleli is doing great. They ask for a little space and privacy while they recuperate and prepare to take Kepaleli home."
In October last year Adams announced she and husband Gabriel Price were expecting their second child. Then in December they revealed they were expecting a boy, which was due in mid-April.
This morning Adams wrote on Instagram: "Kepaleli Tava Sydney Adams-Price. Welcome to our family and a safer Aotearoa. A little early - just as keen as mum and just as healthy. Happiest parents in the world."
Adams and Price, childhood friends, married in 2016 in an extravagant island ceremony.
The pair welcomed their first child, daughter Kimoana, in October 2017. Adams later opened up about her fertility problems to help others in the same position.
Just six months after Kimoana's birth, Adams was back in the throwing circle where she won a silver medal at the Commonwealth Games on the Gold Coast.
The 34-year-old is targeting her fifth Olympic Games at Tokyo 2020.
"The risk of completing our family and training for the Olympics... I don't want that. First and foremost for me was actually giving Kimoana a sibling and completing a family. For us this is it," she said in October last year after announcing she was pregnant with her second child.
"I don't want to come end of Tokyo, look back and have any regrets.
"I don't want to be one of those should've, would've, could've. I've got the opportunity now, I need to take it. It's the same with sport, if you've got the opportunity, take it."
