Read as much formal, nonfiction, "expository" writing as possible and try to absorb the style. The New York Times, or the articles in Wikipedia are good models. Most of the English you learn in an English course is formal.
One detail to notice is that in academic writing, you almost never see the word "I." The passive voice is used heavily. The passive voice conveys a feeling of distance, lack of emotion, cool rationality. This is bad in most writing, but considered appropriate in academic writing.
Active voice: "In academic writing, you almost never see the word 'I.'"
Academic style: "In academic writing, the word 'I' is almost never seen."