As for a wedding date, West, 36, said the couple are aiming to marry sometime "next summer".
The rapper pulled out all the stops for the surprise proposal on Kardashian's 33rd birthday on October 21.
He hired out the entire AT&T Park baseball stadium in San Francisco for the occasion, and asked Kardashian for her hand in marriage in front of friends and family.
West first asked Kris Jenner, Kardashian's mother, for her blessing, E! Online reports, before he got down on one knee and proposed to the socialite with a 15-carat diamond ring by celebrity jeweller Lorraine Schwartz.
The singer also arranged for the words "PLEEEASE MARRY MEEE!!!" to appear on the stadium's scoreboard, while a 50-piece orchestra played Lana Del Rey's Young and Beautiful, and Keri Hilson, Ne-Yo and West's Knock You Down.
Asked whether he had any pre-proposal jitters, West admitted: "I was nervous a little bit. But more about everything being on cue."
He added, "They didn't have the lights exactly how I wanted them to be. I'm arguing with the guy who put it together. He's talking to me like, 'man they need to be more romantic.' I'm like, 'It's a baseball field. What are you talking about? If I wanted to be romantic, I would have went to a small restaurant.'"
West also spoke about the finger bling he chose for Kardashian.
"[Kardashian] knew I was eventually going to ask her to marry me," he said. "I just had to get that ring right. I worked with four different jewellers. Three rings were made and only one hit the ringer and that was Lorraine [Schwartz]'s. I actually changed the ring the night before. The ring was less than four hours old when I gave it to her."
'I GOTTA APOLOGISE TO THE RACE OF MALES'
The modest devil was also in an apologetic mood during the two-hour confab.
"I gotta apologise to the race of males for turning it up so much," West quipped of raising the bar for other men who are planning on popping the question.
"I wanted to marry that girl from the first time I saw her," he gushed about Kardashian. "I just had to wait through a bunch of relationships to finally get my chance...it's just patience. You know with certain things, you're like, 'Yo, this is what's right for me, and this is what I should be doing.' And you gotta be patient."
And don't rule out the couple televising the vow-swap - for the right price.
"I would take as much as possible, if someone's gonna pay me to broadcast that," West told the host. "What's official for everybody in this room and everybody on this globe right now is them bills. If you can help out with those bills, because you know me and Kim are in the exploitation business. We get paid to exploit ourselves."
He added, "Imma give my daughter the opportunity to choose when she wants to be exploited. That's the reason we didn't take any money for any baby pictures."
Kardashian told People.com last week that she's left wedding planning up to West so far.
"We honestly haven't had a moment to talk about it or even breathe, so we haven't really talked about it, but whatever he wants," she said.
Kardashian also said the proposal, despite reports to the contrary, was an "absolute, complete surprise," adding, "I was shaking so much, shaking the entire time. Like, 'Is this really happening?' It was like an out-of-body experience."
"It's a blur..." Kardashian dished to Extra while flashing her engagement rock. "I think he has the most amazing taste in the world and I think this really proves it."
This will be the third marriage for Kardashian, who was previously wed to NBA player Kris Humphries for just 72 days, and before him to music producer Damon Thomas.
West and Kardashian, who went public with their romance in 2012, welcomed daughter North West in June.
Check out West's interview below:
NOTABLE NUGGETS
And finally ...
* "I'm not brilliant with babies" - Simon Cowell talks fatherhood.
* Lady Gaga gives Kelly Osbourne a birthday cake, Kelly tells "hypocrite" Gaga where she can stick it; eventually backtracks.
* "It's Britney, witch!" - Spears recites Vincent Price's Thriller monologue for Halloween spoof; Spears' songs used to scare off Somali pirates.
* Class act: Beyonce photobombs fan taking a selfie in concert.
* Jonas Brothers declare "it's over for now".
* You're never too old to twerk, apparently: Hugh Hefner and wife Crystal Harris deck out as Robin Thicke, Miley Cyrus for Halloween.
* Lisa Kudrow is really glad she had a nose job as a teenager.
* Jane Seymour is making her breakup from hubby James Keach official.
* TMI: Keith Urban says he and Nicole Kidman keep romance alive by sexting.
* Miranda Kerr and Orlando Bloom put on a united front after split; the Sunday People drags teen titan Justin Bieber into the mix.
* Must watch (while you can): Star Wars blooper reel makes its way online. Harrison Ford stumbles over his lines and eats a headset, Stormtroopers clumsily navigate through a hole in the set, and Sir Alec Guinness gets a face full of Chewbacca's arm. Check it out here.
- Rumour Has It
