A source told the magazine the 36-year-old rapper was "supposed to attend his listening session" for his new album event Friday night.
"Kanye canceled about 15 minutes prior [to the playback] to be by Kim's side," the unidentified source said.
Kardashian, 32, "looked very exhausted and tried to be incognito" when she entered Cedars-Sinai Medical Center in West Hollywood, the source said.
"Kanye seemed very supportive. It looked like support in pain and labor."
E! network, which carries Kardashian's reality TV show, confirmed West was with her for the birth.
E! said the couple hadn't divulged their daughter's name, but that Kardashian told friends it "will start with a 'K,'" and the middle name could be Donda, after West's late mother.
Celebrity Breakups and divorces of 2014 [PHOTOS]