The reality star gave birth to the the little boy on December 5 and the couple revealed its choice of name for him in a post on Kim's website and app.
"SAINT WEST," Kardsahian posted on Twitter.
There was no mention of a middle name, despite reports that Kim would add her late father Robert to her son's moniker.
The news follows months of speculation the couple would choose another compass point for the little boy, after naming their two-year-old daughter North.
Kim Kardashian West, Kanye West welcome baby boy