The 33-year-old Kardashian said she is "thankful, excited, nervous, eager, overjoyed and scared all in one" and called the pregnancy "my greatest dream realized."
Kardashian is the younger sister of Kim Kardashian West, who is also expecting a baby by surrogate.
Her 26-year-old boyfriend, Thompson, plays centre-forward with the Cleveland Cavaliers.
The couple's pregnancy had been rumoured for months. Khloe Kardashian said in her post Wednesday that they intentionally kept the news quiet so they could "enjoy this between our family and close friends as long as we could privately."
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