Williamson and wife Sarah Raheem welcomed a baby girl into the world, with Williamson announcing the news on Instagram this afternoon.
"Overjoyed to welcome a beautiful baby girl into our family," Williamson wrote.
The 30-year-old had revealed the impending berth after the first test against the West Indies earlier this month.
"It's a very exciting time in anybody's life and it certainly is in mine," Williamson said.
Williamson missed the second test against the West Indies to be with Raheem as the pair awaited the birth, with the Black Caps batsman having flown back and forth between Wellington and Tauranga before returning to Tauranga to be with his wife ahead of the test.
Black Caps coach Gary Stead said at the time that the whole team was supportive of Williamson.
"Family comes first. Kane's not the first player to miss a test match because of an impending birth and he won't be the last," Stead said.
"Worst-case scenario Kane misses some matches.
"As a dad, as a parent, you only get that opportunity once in your life to be there for your (first) child's birth and I know that it's important for Kane too.
"At the end of the day we play cricket and other things are much more important."
Raheem is a qualified nurse who studied at the University of Bristol in England.
