The App Store review office at 1 Infinite Loop has officially frozen over: we’ve gotten word that the official Google Voice application is on its way to the iPhone in the next few weeks. In fact, we’ve heard from a source close to Google that it’s already been approved — Google just needs to revamp the application to work with the iPhone 4 and iOS’s multitasking capabilities. If you’re a Google Voice user and you’re on an iPhone, this is great news.

It’s been a long, long road to get here. Last July, we broke the news that Apple had blocked the official Google Voice application, which eventually sparked an FCC inquiry into the matter. Apple claimed that the application “duplicated existing functionality”, which didn’t do much to convince anyone as it subsequently accepted similar apps. Nothing happened for well over a year, and the odds of Google Voice ever making its way to the iPhone, at least as a native application, seemed bleak.

Everything changed on September 9, when Apple published a set of guidelines telling developers which applications would not be allowed into the App Store — and none of the rules seemed to apply to Google Voice. Rumors started swirling that third-party Google Voice apps might soon make their way to the App Store, and sure enough, a handful of applications have since been approved.

But the existing applications, nice as they may be, are all provided by third parties. We haven’t gotten the chance to use the official Google application, but it’s possible that it will include functionality that the others don’t. Namely, push notifications for inbound SMS and voicemail messages (Google doesn’t provide an API for these, so third parties would have to route these messages through their own servers to offer push notifications).

Reached for comment about the upcoming iPhone application, Google offered this non-answer of a statement: