The tiny tot was delivered via an unplanned C-section on Saturday (15 February), Us Weekly reports, and Jason and Jenny are already besotted with their new bundle of joy.
In fact, the couple have been so excited about Sid's arrival that they've kept fans updated every step of the way, posting photos and videos of their journey to parenthood over the weekend - including Jenny going into labour and travelling to the hospital!
In one short video clip uploaded to Instagram yesterday (18 February), we can see Jenny sat in the car while heading to the hospital.
The clip is captioned, "February 15th, 2014 3:00am #babybiggs" and the actress is heard saying, "It hurts so bad" after Jason reminds her to pack her book.
Another three videos show Jenny as she battles with her labour pains, although these are soon followed by a fourth clip captioned, "February 15th, 2014 5:33pm #babybiggs", in which she and Jason reveal that their son has finally been born.
Speaking to his wife after the birth, Jason says: "You did amazing baby, I'm so proud of you... he's pretty damn cute."
The couple - who married in 2008 - then shared a snap of the newborn sleeping in an adorable little hat and wrote: "Sid Biggs. Full head of hair, huge penis, 10k twitter followers. #babybiggs."
Jenny also posed for a photo with a dog dressed up as a doctor - complete with a stethoscope - and thanked the hospital staff for their help.
She added the caption: "We are incredibly grateful to all the nurses and staff at Cedars Sinai! Everybody was top notch:) particularly fond of this resident. #babybiggs."
The last picture (for now!) shows Sid's tiny feet, as the new parents cut off his hospital tags.
Jason and Jenny wrote beside the snap: "Once you remove the tags, there are no refunds! #storecreditonly #babybiggs."
Hollywood funny guy Jason announced that he and his wife were expecting a baby last July during an appearance on US chat show Chelsey Lately.
He broke the news unexpectedly while commenting on the size of Jenny's boobs, saying: "Her breasts are very big these days. Would you like to know why? Cause I put a baby in her belly!"
More celebrity babies born in 2014:
Copyright: Rex Features WENN/Matthew Taylor/Daniel Deme/Josiah True/Matthre Taylor/Joe
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