Quote Originally Posted by Simon000001 View Post
... я буду студент, переехавший по обмену в университет ...
Так лучше?
студент по обмену - it's kinda term in Russia meaning that you're a student who's gonna to move (or have moved already) to and study at a Univercity, College etc (especially foreign ones) as their student temporarily. So I'd suggest:

Я стану студентом по обмену и перееду (уеду) в университет ... (....буду/стану учиться в университете....)

I hope this helps