Depends on what you mean by "Tanna".
Generally, in classic sources, the Anshei K'nesses HaGedola refers to the generation of Ezra and Nechemya that built the new community in Israel. Then Shimon HaTzaddik was the last surviving member of that generation. (This creates some chronology problems, but let's take this as a given anyway.)
The Tannaim is the name for the Sages of the Mishna. That is, the earliest point that can be considered a source for the statement compiled into the Mishna. What results is that this whole thing is a matter of classification. Shimon HaTzaddik was the bridge between the Anshei K'nesses HaGedola (which would be the end of the Biblical/Prophetic era) and the Tannaim (the Mishnaic era). So which does he belong to?
The Rambam seems to count him as the first of the tannaim (or "Chachmei HaMishna"). Abarbanel considers him part of the previous generation (that of Nechemya) and starts the generations of Tannaim with Antignos. Machzor Vitry doesn't start considering anyone Tannaim until Hillel and Shammai; everyone before is just "the Sages that lived from generation to generation" between Biblical and Mishnaic times.
The point is, though, that it doesn't really matter. Everyone cited above agrees about who Shimon HaTzaddik was, when he lived, and what he said. It's just a matter of when do I start calling people "Tannaim"? And that's just about keeping track of classifications.