The former The Voice coach's representative confirmed the big news to Us Weekly, revealing, "The family is happy and healthy!"
Lasichanh, 36, reportedly gave birth earlier this month.
Since Williams embraces privacy in his high-profile career as a singer, songwriter and reality TV star, no additional details regarding the babies' names or sex have been released at this point.
Lasichanh's pregnancy was confirmed back in September. The model and Williams, 43, attended a dinner hosted by Chanel in West Hollywood, CA, that month when the mom showed off her growing baby bump.
The Voice coach and Lasichanh reportedly dated for five years before they got married in October 2013 in Miami, FL.
The couple's three new babies join their eight-year-old son Rocket Ayer, whom an Us source previously called "adorable" and a "genius."
In 2014, Williams revealed to Oprah Winfrey where the name Rocket came from.
"In the same way the Indians named their children behind a force or animal or element, we named him after a man-made machine that was meant to go up, meant to ascend," Williams explained. "Metaphorically it was because of Stevie Wonder's 'Rocket Love,' Elton John's 'Rocket Man' and Herbie Hancock's 'Rockit' -- all of my favorite musicians."
Williams has also gushed to different media outlets about how Rocket is his best friend and his son teaches him a lot about technology.
Williams began serving as one of four coaches onThe Voice's seventh season. He stuck around for four editions until he was replaced by Alicia Keys for Season 11. It's likely Williams will return at some point for a future season.