E! News first reported that the rapper popped the question on Monday - the reality star's 33rd birthday - at AT&T Park in San Francisco.
West reportedly paid at least $200,000 to rent out the stadium. He had 50 musicians playing as family and friends streamed out of the dugouts.
The couple welcomed their first child, daughter North West, in June.
A photo posted on Instagram shows Kardashian showing off a diamond ring with a stadium screen that reads "PLEEEASE MARRY MEEE!!!" in the background. Her caption says "YES!!!"
This will be the third marriage for Kardashian, who filed for divorce from basketball star Kris Humphries in 2011 after just 72 days as husband and wife. Her first marriage was to music producer Damon Thomas in 2000.
The Associated Press contributed to this report.