West, who will play the 2013 MTV Video Music Awards on Sunday, noted he wanted to show the picture of his baby girl, born in June, on the season finale of her grandmother's talk show, making the reveal especially personal.
Before Friday's episode, Kanye, Kim and their daughter, North, reportedly attended the funeral of Kanye's grandfather in Oklahoma, marking the family's second public appearance this month. Both those times, however, the baby was covered up.
During the one-hour sit-down, Yeezy opened up about a number of subjects, including his history with the VMAs as well as his much-discussed personal life.
"That I could have people saying, 'You know, this is going to damage your cred as an artist or as a designer.' And I say, 'I don't care, I love this woman," he said. "And [Kim's] my joy and she brought my new joy into the world. And there's no paparazzi and there's no blog comment; there's nothing that's going to take that joy from me."
The big reveal comes two days before the G.O.O.D. Music rapper is slated to take the stage at the VMAs when they go live Sunday at 9 p.m. ET/PT from Brooklyn's Barclays Center. He will perform his Yeezus track "Black Skinhead." Other big performers include Katy Perry, Lady Gaga, Justin Timberlake and Robin Thicke.