"Closure: Like time suspended, a wound unmended - you and I. We had no ending, said no good-bye. For all my life, I'll wonder why," read the reality star's post.
Kardashian, who is believed to be dating her ex French Montana again, is said to have called Odom to congratulate him on Thursday.
Kardashian and the basketball star had been married for four years when they separated in August 2013 amid rumors Odom had been unfaithful and was dealing with a drug problem. Kardashian filled for divorce in December, but sources recently revealed Odom has been refusing to sign the papers.