The Lord of the Rings: The War of the Rohirrim won't be the first time a work by J. R. R. Tolkien gets an animated adaptation. Many fans will undoubtedly remember the 1978 animated movie with varying degrees of fondness.
Over the years, you might have even seen media that tackle stories not encountered in the main story, such as the independent film Born of Hope (2009) which tells the story of Aragorn's parents. But it's not every day that we see a Lord of the Rings adaptation that does not draw directly from either The Hobbit or The Lord of the Rings stories, and, until the Amazon tv show comes out, we aren't used to this. So, is The War of the Rohirrim canon?
The short answer is yes. The Lord of the Rings: The War of the Rohirrim is canon in the Tolkienverse simply because the story it's going to tell is in The Lord of the Rings book, so a reread before the anime comes out is not a bad idea!
The War of the Rohirrim will tell the story of Helm Hammerhand, a legendary king of Rohan, and it will unfold 250 years before the events we know and love. Even if you don't recall reading about Helm, you surely remember Helm's Deep which is name after him.
Information about Helm Hammerhand can be found in Appendix A towards the end of The Lord of the Rings. That section includes details about the kingdoms of Numenor, Gondor, and Rohan, and their rulers.
The kings of Rohan are divide into lines, and a line ends when a king is succeeded by someone other than his son. Helm is the last king of the first line, as both his sons were killed and he was succeeded by his sister's son, Fréaláf.
From the above, it's understood that The Lord of the Rings: The War of the Rohirrim is canon; of course, to have enough content for a movie it will probably be significantly expanded, but whatever additions are made are unlikely to contradict the canon. We will update this space when more details about the plot of the anime movie are available, but what information we currently have suggests that Helm's story will be tragic – as they often are in Middle Earth.