West popped the question at Kardashian's 33rd birthday party in San Francisco Monday night with a 15-carat diamond ring.
West rented out the entire AT&T Park stadium, home of the Giants, for the occasion and proposed in front of friends and family members.
He also arranged for a 50-piece orchestra and a fireworks display.
The couple has a daughter named North West who was born in June.
A photo posted on Instagram shows a screen at the stadium that reads "PLEEEASE MARRY MEEE!!!" - in typical West font - above a black-clad orchestra. Another shows Kardashian showing off a diamond ring with a smiling West behind her.
The Kardashian clan has a series of reality shows on E!, but the network said Tuesday it did not have cameras at the stadium to capture the moment.
Khloe Kardashian seemed to celebrate on Twitter when she wrote: "Tears of JOY!!!!!!! Wow!!!!!!" She also tweeted: "Wow!!!!! Am I dreaming-!?!" Kimye were quiet on Twitter.
Kardashian was previously married to NBA player Kris Humphries. Their divorce was finalized in June after they were married for 72 days in 2011. Her first marriage was to music producer Damon Thomas in 2000.
West is currently on a tour with Kendrick Lamar. "The Yeezus Tour" will visit the SAP Center in San Jose on Tuesday night. Earlier Monday, he attended the Hollywood Film Awards in Beverly Hills, presenting Steve McQueen with the Hollywood Breakout Director Award.
The Associated Press contributed to this report.