This would not be a direct translation, although it would mean the same thing in context. Also, your translation implies that you already know the boy, whereas the original sentence implies that you only know him as "the boy next to me."
I would translate that as "Pojken är bredvid mig och läser en bok." (Literally: "The boy is next to me and reads a book.") The Swedish gerund, though it exists, isn't really as common as the English and often has to be changed somehow or it'll sound unnatural.