However, Tolkien himself intended for it to be one. The publisher wouldn't have it, insisted on splitting them up, and Tolkien basically argued with them right up to the end. (And he was not happy about the third book being called
Return of the King. He wanted it to be titled
War of the Ring, but again, the publishers didn't want "war" in the title.)
So, it
is (technically) one book (officially).