This man is Alex Roldan, a hairdresser who's been working with Kris Kardashian since the 80s -- the same decade in which she had an affair while married to Robert Kardashian.
Here's another Instagram photo of Khloe taken today (for those who think the above picture looks photoshopped):
So wait: is this guy really Khloe's dad? They certainly look similar. My guess: this Alex character really is Khloe's father -- but E! would like for us to wait and watch the big reveal on the new season of "Khloe And Lamar."