Alexis' representative confirmed that the actress gave birth to the baby last fall. No further details have been released, reported People magazine.
In November last year, reports suggested the 34-year-old actress and Vincent were preparing to welcome their first child, but they never confirmed the rumours.
When the couple made its first public appearance following the reports at the Screen Actors Guild Awards in January, Alexis hit the red carpet without a visible baby bump.
The actress then went to work on the upcoming "Gilmore Girls" revival in February, prompting fans to believe the baby news was just a gossip item.
More From This Section
When asked what his experience was like to work with grown-up child star Alexis again, now she's an adult, Scott said, "She's really blossomed as a woman and now she's a proud new mother and married and happy.
"I remember her as an 18-year-old kid, fresh out of college, coming into Hollywood and being a little overwhelmed. She's just the most likeable, intelligent person and adorable human being. She hasn't changed at all. She looks the same."
Scott, 57, became a first-time father to a baby boy in June, 2014.
This isn't the first time Alexis and Vincent have kept a major secret. The couple wed in a private California ceremony in June, 2014, but news of their marriage didn't surface until August.
The two actors began dating in 2012 and announced their engagement in 2013.