There's only one catch - unlike the original mobile authenticator found in the App Store, these new versions aren't free. The prices vary depending on your country due to PayPal conversion rates, but they amount to roughly $1 (it's €0.50 in parts of Europe).
Despite the need to purchase it, we at WoW.com can't recommend it highly enough. Account security is an important thing, particularly with the rampant account hacking and phishing going on these days. Now that it's available to use in a wide variety of platforms, there's little reason not use the Battle.net mobile authenticator. A dollar is a very small price to pay for that additional layer of security.
Editor's Note: Apparently now the download is showing as "Coming soon" for US/EU carriers. It was showing as up before, but now is not. We blame the Gnomes. Or Ghostcrawler.
Thanks to Medros from All Things Azeroth for the tip!