It doesn't seem to be related to any other documented languages. Being endemic to Sauron's realm, with him persisting through the Ages, it would not likely have diverged naturally from another language anyway.
There is this related question, which deals with how Tolkien the author arrived at the Black Speech. The answer includes this quote:
The Black Speech was not intentionally modeled on any style, but was meant to be self consistent, very different from Elvish, yet organized and expressive, as would be expected of a device of Sauron before his complete corruption.
That answer doesn't address how the language came to be; but the emphasized portion implies Sauron developed it himself. That's certainly reasonable though I'd be curious when and why. Did Tolkien expound on that anywhere else?