When using the word "since," it sounds more natural to use the present perfect progressive ("I have been studying..."). "Since" implies there is an action continuing into the present and would not be as compatible with the present perfect tense ("I have studied...")
The following would be a little more accurate:
1. I have studied English (before). (completed, note: the term "since" is not used here)
2. I have been studying English since 1999. (continuing into the present)
Source: myself, American English