Williams welcomed McLaurin Clement Williams last month and the family shared photos and details with People magazine.
McLaurin was Robin Williams' middle name. Zak and his fiance, Olivia June, will call the little guy Mickey, they said.
Zak's half-sister Zelda posted a sweet message and pics of the new baby boy!
"Meet Mclaurin Clement Williams, aka Mickey, aka Dr. Baby! He’s a squishably cute pterodactyl cooing tiny wonder and I love him so much already big shoutout to Mickey on being the fastest swimmer, and huge congrats to @heyoliviajune and my big bro @zakpym on creating this little joy (and poop) factory!" Zelda wrote.
June also posted pics and the new mother had a lengthy message about her new bundle of joy.
"Introducing you to my little family! My fiancé, Zak, and I were so happy to welcome baby McLaurin to the world on May 22nd. We are beyond thrilled he chose us to be his parents, and obviously think he’s the best, smartest, and cutest baby ever!!" she wrote.
The "Aladdin" star died in 2014 at the age of 63. Williams was battling depression and the early stages of Parkinson's disease.
Zak Williams is now a mental-health advocate and entrepreneur, while his fiance is a CEO, women's advocate and extremely successful venture capitalist.
Zak Williams took the lead in helping the family move forward after his father's death.
"We're acclimating to the new normal. Everything is step by step," he told US Weekly in 2014. "Dad had almost a childlike love, and he shared that love with people, with everyone. And that ability to love, and that ability to be generous and giving and kind is something we would want to share with future generations."