Firstly, having "the" in front of Canadian writer is entirely optional.
You should say "was published," the past tense, rather than "has been published," the perfect, here.
As a native English speaker, I understood immediately that you were referring to the book, but I think it might even be better to do something like this:
Today I finished reading a book, titled "Fifteen Dogs" by Canadian writer André Alexis, which was published in 2015.
An even better way to do this would be this:
Today I finished reading Fifteen Dogs, a book by Canadian author André Alexis, which was published in 2015.
Or you could try splitting it into two sentences. There are many ways to do this.