According to the Stuff website, Williams missed his new club Toronto Wolfpack's Super League defeat to Wigan in order to fly home to New Zealand as wife Alana was due to give birth.
In a photo posted on Friday on social media, Williams is seen holding the child in his arms while dressed in blue scrubs with a red hairnet - while donning a large grin.
"Alhamdulillah Alhamdulillah Alhamdulillah ! Baby & mum are healthy and well," Williams wrote on his Instagram account.
"The stress levels aren't as high 4th time around, but the love we have for this child is the same."
The baby, whose name is yet to be confirmed, is the Williams' second son after Alana previously gave birth to Zaid. The couple also have two daughters - Iman and Aisha.
Williams played his 58th and final Test for New Zealand in the 2019 Rugby World Cup bronze-medal match against Wales before signing a NZ$10 million, two-year contract with the Wolfpack.
The Wolfpack are yet to win a match in their maiden English Super League season.
Sonny Bill WilliamsGetting that skin to skin. ❤️🤲🏽 #myson #AlwaysAlhamdulillah
Sonny Bill WilliamsAlhamdulillah Alhamdulillah Alhamdulillah ! Baby & mum are healthy and well. The stress levels aren’t as high 4th time around, but the love we have for this child is the same. @lanamarieewilli I appreciate you my love ❤️