Reality TV star Kim confirmed the news on her website with a statement that said: "Mother and son are doing well."
The superstar couple's daughter, North West, was born in June 2013.
Kim announced she was pregnant again in an episode of her show Keeping Up with the Kardashians at the end of May.
She revealed their second child would be a boy in a Father's Day tweet to her husband back in June.
There's no news on the name yet, but Kim has previously said South West was not in the running.
"I don't like South West... North will always, you know, be better and be more… she has a better direction," Kim said in an interview with National Public Radio in America.
Kim tweeted photos of herself and her baby bump hours before the birth.