"It's true!! Kanye and I are expecting a baby," Kardashian, 32, wrote on her personal blog.
"Looking forward to great new beginnings in 2013 and to starting a family," she added.
Kardashian began dating West in April, some six months after filing for divorce from basketball player Kris Humphries. The two were married for 72 days following a lavish, made-for-TV wedding. Their divorce has yet to be finalized.
Kardashian is about 12 weeks pregnant, according to U.S. media reports.
Fans and family took to Twitter to congratulate the celebrity power couple, and to speculate whether the new baby's name would begin with a K, in line with Kardashian family tradition.
"Been wanting to shout from the rooftops with joy and now I can!" wrote Kardashian's sister Kourtney. "Another angel to welcome to our family. Overwhelmed with excitement!"
Kardashian's brother-in-law, basketball player Lamar Odom, who has been open about struggling to have a baby with wife and "The X Factor" host Khloe Kardashian also tweeted his congratulations.
"I'm excited for Kanye and my sister!" said Odom. "There's nothing like bringing life into this world! Let's keep God's blessings coming!"
West, 35, was first to announce the news from the stage at a concert in Atlantic City on Sunday, singing, "God brought us a whole new plan, baby. 'Cause now you're having my baby."
Kardashian, who rose to fame five years ago for her appearances in reality TV show "Keeping Up with the Kardashians," was the most-searched person on the Yahoo! website in 2012. (Reporting by Eric Kelsey; Editing by Jill Serjeant and Cynthia Osterman)Kim Kardashian, Kanye West, Kris Humphries, Lamar Odom, Hollywood