They announced the birth on Kim's website saying, "Mother and son are doing well."
The due date was Christmas day, but as we told you ... Kim just had a feeling he was coming early. She posted a selfie when her contractions started last night, saying ... "Ready whenever you are. LOL"
Now, the real work begins -- what to call this kid! TMZ broke the story, Kim and Kanye were panicking because they had not come up with a solid pick for a name yet.
May we make a suggestion? Y'know this is how Kanye feels right about now ...