West made the announcement during a concert in Atlantic City last evening, saying "Stop the music and make noise for my baby mama."
The fans have congratulated the couple on Twitter which was followed by tweets from Kim's sister Khloe Kardashian.
"KIMYE!!!!! Keeping secrets is hard with so many family members! Especially when you are so freaking excited!!!!! LOVE is everything!!!!"
Their mother, Kris Jenner, tweeted, "Oh BABY BABY BABY!!"
Kim and Kanye began dating in April 2012. She split from second husband Kris Humphries in 2011 after just 72 days of marriage. Kim is technically still married to Humphries as their divorce hearing is scheduled for February 15.
West has been accepted by the family and has made appearances on its reality show 'Keeping Up With The Kardashians'.