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Fans and family took to Twitter to congratulate the celebrity power couple.
"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!"
According to E! News, West, 35, announced the news from the stage at a concert in Atlantic City on Sunday.
Kardashian, 32, 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.
She married basketball player Kris Humphries in August, 2011, in a lavish, made-for-TV wedding, but the couple divorced just 72 days later.