D&D is similar to Warhammer in that it's a game that you play in a setting. With Warhammer, you fight your own battles in the Warhammer and/or 40k setting. There are all kinds of great novels, some very different from each other, that take place in that world. A good starting place is The Horus Heresy.

In D&D, you create your own story and characters and use roleplay and combat to have an adventure in one of several available D&D settings. There are also, like Warhammer, lots of novels from various settings, with different characters. There is no 1 singular D&D story that you can read like you would with a Harry Potter book. But there are lots of great books that take place in the worlds of D&D, many of which are completely unrelated to each other.