Scroll down for video of Kim discussing the shock cover.
The famous couple met up with Anna Wintour for dinner on Tuesday night, at New York City's exclusive eaterie the Waverly Inn.
Earlier in the evening, Kim revealed that it came as a total surprise to her when she was told her wedding-themed shoot with Kanye and baby North would take a starring role.
"I knew it was happening, obviously I was shooting it, but I didn't know it was going to be the cover," she told Seth Myers.
"It was such a secret – I didn't tell my sisters, I didn't tell anyone. My mom knew because we had to use parts of her home. So it was this top secret mission trying to keep out all of my sisters and everyone from knowing."
The reality star said keeping the shoot under wraps was extremely difficult, but in the end she managed by using Kanye as an excuse.
"They were a little suspicious," she says of her famous family. "But I just told them Kanye was shooting something at my mom's house and it was really private and just kind of blamed it on him.
"I don't keep the best secrets, I have the biggest mouth ever."
Kim said being chosen for the front of the style bible was "such an honour". Their appearance there, she said, marked a lot of firsts in the magazine's history.
"There are a lot of firsts. Kanye's the first rapper to be on, I'm the first reality person to be on, we're the first interracial couple." All of these mean so much to Kanye and I.