The 34-year-old and his wife Tasha McCauley welcomed their first child over the weekend, according to Us Weekly.
A source told the magazine, "Everyone's happy and healthy."
The very private couple hadn't publicly revealed the pregnancy after also having married secretly last year.
Tasha, who is the founder of a robotics company called Fellow Robotics, first started dating the 500 Days of Summer star back in 2013. They kept their relationship on the downlow and married at their home in Los Angeles on December 20th, 2014.
Besides his duties as a new father, Joseph has quite the busy few months with three films set to be released.
First up is the biographical drama The Walk, which reenacts Phillipe Petit's perilous 1974 high-wire act across New York's Twin Towers. Directed by Robert Zemeckis, the film hits select theaters on September 30th.
Fans can next see him co-star with Seth Rogen and Anthony Mackie in the comedy The Night Before, due out November 25th.
And a month later, on Christmas Day, he stars as Edward Snowden in Oliver Stone's biographical thriller Snowden.
Looks like Joseph and Tasha are going to need a sitter on speed dial, stat.