"Congrats Sonny to you and the family. He's a beaut," said on Twitter user.
In another photo posted on Friday, Williams was holding the child in his arms while dressed in blue scrubs with a red hairnet while donning a large grin.
"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."
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Posted shortly after 1pm, within 10 minutes the post had already racked up more than 5000 likes.
Williams recently relocated to Canada after signing a contract with Super League team the Toronto Wolfpack.
However, he returned to New Zealand for the birth of his fourth child.
And several sports stars have congratulated the Williams family on the latest arrival.
"Congrats bro. Awesome news," wrote All Blacks loose-forward Sam Cane.
"Congrats to you and your family bro," said All Blacks hooker Codie Taylor.
Meanwhile, former NRL star Braith Anasta, All Blacks loose-forward Ardie Savea and former Wallaby flyhalf Quade Cooper posted heart emojis.