Joseph Gordon-Levitt's wife, Tasha McCauley, has given birth to their first child.

Joseph Gordon-Levitt

Joseph Gordon-Levitt

The 'Snowden' star and the entrepreneur, who quietly married during an intimate ceremony at their Los Angeles home in December, are over the moon after welcoming a baby boy into the world last weekend.

A source close to the '500 Days of Summer' star, 34, told Us Weekly magazine: "Everyone's happy and healthy."

The couple, who kept Tasha's pregnancy a secret, have no plans to release their son's name, but another insider told PEOPLE.com: "The family is all happy and healthy."

The duo started dating in 2013 after being introduced by mutual friends, but Joseph, who has always been tight-lipped about his private life, previously admitted Tasha, who is currently a business director at GeoSim Systems, isn't interested in being in the spotlight.

The former '3rd Rock from the Sun' star once told Howard Stern: "I have a girlfriend, but I tend not to really like to talk about it in public. The girl that I'm with, she really doesn't want to be a part of that."

Shortly after they got together, a source revealed: "She's very intellectual and a creator, which he finds very attractive. It's a really healthy and normal relationship."