According to E! News, Kanye, 36, hired out the AT&T Park stadium in San Francisco for the occasion.
He then presented the mother of his child with a 15-carat diamond ring by celebrity jeweller Lorraine Schwartz.
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A few hours earlier, Kanye appeared on stage at the Hollywood Film Awards in Beverly HIlls, where he made reference to a quick commute to San Francisco — but said nothing about a marriage proposal.
Kim and Kanye, who went public with their romance in 2012, are parents to four-month-old daughter North.
This will be the third marriage for the TV star. In 2000, Kim, then 19, married music producer Damon Thomas but the couple split four years later. Then in August 2011, she wed basketball star Kris Humphries; their marriage famously lasted just 72 days.
Kim and Kanye have been the subject of marriage rumours for a while, with Kim's mum Kris Jenner telling E! News back in August 2012 that the family "adored" Kanye, adding, "We think they make an amazing couple. We just want them to be happy".
"Marriage is something I know that we both want in our future, but I don't have this sense of urgency about it," Kim herself told Cosmopolitan in February. "I have this best friend who understands me and helps me through all my tough experiences, and vice versa, you know? It just feels like this is it for me."