Actually how you'd say it in Japanese would depend on the context.
Maybe I'd say "ありがとうございます/Arigatou-gozaimasu (To thank for the support that's being given or will be given)"/"ありがとうございました/Arigatou-gozaimashita (To thank for the support that was already given)".
My dictionary gives "ご助力感謝いたします/Go-joryoku kansha itashimasu" as a translation for "I appreciate your support/help", btw.