"They're over the moon!" a source close to the first-time parents-to-be tells Us. "Kanye always wanted a girl."
Kardashian, 32, and West, 35, began dating in April 2012 and announced they were expecting on Dec. 30.
The couple's daughter, due in July, will no doubt be very well dressed. "If anyone knows Kanye, they just know how into fashion he is, and I think he's going to have things specially made," Kim said of the rapper and fashion designer on Jimmy Kimmel Live in January. "So I don't think hand-me-downs are going to work."
"He is so excited," she gushed. "It's really cute how excited he is."
Until the baby arrives, Kardashian is focused on taking good care of her body.
"I used to always say I can't wait to get pregnant because I will just eat whatever I want, but it's completely different," she told the spring issue of Du Jour magazine. "I'm like, OK, I want to eat as healthy as possible. Though lately I've been watching shows like I'm Pregnant and Addicted to Meth. It definitely makes me feel better if I'm wanting one sip of Diet Coke or, you know, too much sugar. I'm like, This woman is on meth."
Kardashian and West's baby girl will join cousins Mason, 3, and Penelope, 7 months.