Kardashian mum Kris Jenner linked to both tweets on her Twitter account. She was scheduled to be a presenter at Sunday night's Daytime Emmy Awards.
The reality TV star's pregnancy was almost as anticipated as the royal pregnancy of Kate Middleton, who is due in mid-July. That's about the time the Kardashian baby had been due.
The 32-year-old has often been photographed since announcing she was pregnant, opting to continue to wear designer clothing. In April she said that she eventually embraced being an expecting mum after getting past "the awkward phases and stages".
The couple had initially kept the baby's gender a secret, but the sex was revealed earlier this month during one of Kardashian's doctor appointments on Keeping up with the Kardashians.
News of the birth has been swaddled in secrecy. Representatives for West and Kim Kardashian did not respond to emails and calls, nor did any representatives for family members, friends and professional associates.
And all of the weekend media reports on the birth were attributed to anonymous sources.
In a recent interview with The New York Times, West said he didn't like talking about his family or the arrival of his child.
"Like, this is my baby. This isn't America's baby," he said.
- AP