It should. You will need to check to see if you have harness A or B. The following is the guide.
http://www.burgertuning.com/images/T...cation_BMW.jpg
Other thing to check would be the wastegate. Pretty sure you would have the pneumatic, but with checking. If the below link doesn't work, just Google n55 pneumatic vs electronic wastegate.
https://www.google.com/url?sa=t&sour..._G9XrwWJ-GsXoc
If you have B, then the jb4 listed will work.