The actor and comedian, 38, made the big announcement on social media.
"God is truly amazing....Kenzo Kash Hart was born at 1:45am ....He is Healthy & already smiling. Thank you all for your prayers!!!! We love & appreciate ya," Hart tweeted.
Kenzo is Hart's third child; he also has a daughter, Heaven, 12, and a son, Hendrix, 10, from a previous marriage. This is Parrish's first child.
Hart and Parrish announced that they were expecting a child on Mother's Day.
In a sentimental caption on Instagram, Hart wrote, "Celebrating Mother's Day with my beautiful wife. We are laughing at the fact that this time next year we will be celebrating her 1st actual Mother's Day."
The post included two photos, featuring one with Parrish showing off her growing baby bump. Hart also revealed that they were having a boy.
Hart and Parrish wed last August in a ceremony in Santa Barbara, California.
"I know I'm going to hurt the people closest to me who I have talked to and apologized to, being my wife and my kids," Hart said in the video.
Following Hart’s apology, reps for the comedian told ABC News in a statement on Sept. 17: “Someone tried to set Kevin up in a failed extortion attempt. As law enforcement is involved, we cannot comment further as it could affect the investigation.”
An attorney for a woman who said she was "involved" with the comedian in August said someone secretly placed cameras in a hotel suite and recorded images of them, the Associated Press reported.