I think you can definitely add both schools to your resume. It helps show a true representation of your background and serves as a talking point during an interview. When listing your original school, you want to be sure that you aren't misleading in how you list, it so it doesn't appear you completed two degree's. My recommendation would be to list the school, city/state, and years attended. Where your major would typically be listed, you can include "Completed coursework toward X degree". (Or something along those lines.)
Also, since this topic would likely come up during an interview, I would also ensure that you have a good reason and/or explanation to share as to why you transferred schools during your senior year. It doesn't need to be a significant reason, just something that comes across as professional and sincere.