The announcement followed news that their surrogate had given birth May 9, with Kim tweeting last Friday, "He's here and he's flawless!"
It showed a photo of Psalm in bed, with the message, "Beautiful Mother's Day".
Kim and Kanye, 41, have three other children together: Chicago, Saint and North.
At the time the star revealed the baby was "Chicago's twin" in a tweet, and now the world can finally decide for themselves.
But, it turns out that the reality star let the news about baby No. 4 slip while she was drunk at the annual Kardashian Christmas Eve party, which she and Ye hosted this past year. I give up.' Discussing the prospect of surrogacy, she added: 'Kanye was really nervous about the surgery... but I know he would want to have more kids.
She explained that it had meant to be Kim who would appear on the show - however, their surrogate had gone into labour. "So, I feel really calm and at ease..."
Get push notifications with news, features and more.
Thoughts on the little one's name, Perezcious readers??