The reality star posted a picture of the child, delivered via a surrogate, with the caption "Psalm West".
She added: "Beautiful Mother's Day. With the arrival of our fourth child. We are blessed beyond measure. We have everything we need."
The Keeping Up With The Kardashians star has three children with husband West - North, Saint and Chicago.
This is the second time the couple have used a surrogate, having had one deliver Chicago in January last year.
Reality TV star Kardashian West shared the news of the birth on Twitter on Friday, writing: "He's here and he's perfect!"
In another post, she wrote: "He's also Chicago's twin lol I'm sure he will change a lot but now he looks just like her."