On or about ... oops, the battery in my crystal ball just died, and I don't have a replacement.
That's the kind of question that can't be answered until Verizon announces the release date. (And even then, take it with a grain of salt.) Once it's released, it's released in batches, a few hundred phones at a time. (Updating all the S4s on Verizon at once would crash every Verizon tower in the country.) So once it's released, you may get yours the next day, the next month or a few months later.