Joseph Gordon-Levitt on location in Cancun, Mexico on June 14, 2015.
Vera Anderson—WireImage/Getty Images
August 19, 2015 2:39 PM EDT

Joseph Gordon-Levitt has his own little angel.

The Snowden actor is a first-time father after welcoming a son with his wife, Tasha McCauley, over the Aug. 15 weekend, his rep confirms to PEOPLE.

Though the couple won’t be releasing their baby boy’s name, “the family is all happy and healthy,” a source tells PEOPLE.

Gordon-Levitt, 34, wed McCauley, the co-founder and CEO of Fellow Robots, during a quiet ceremony at their home in December.

It’s no surprise the proud new parents kept the pregnancy under wraps. Before tying the knot, Gordon-Levitt admitted he prefers to keep his personal life out of the spotlight.

“I have a girlfriend, but I tend not to really like to talk about it in public,” the hitRECord founder told Howard Stern in 2013, declining to name the lucky lady. “The girl that I’m with, she really doesn’t want to be a part of that.”

— With reporting by Julie Jordan

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