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Apple PR has just announced that Dr. Eric Schmidt, CEO of Google and member of the Apple board of directors since August 2006, is resigning that position.

“Eric has been an excellent Board member for Apple, investing his valuable time, talent, passion and wisdom to help make Apple successful,” said Steve Jobs, Apple’s CEO. “Unfortunately, as Google enters more of Apple’s core businesses, with Android and now Chrome OS, Eric’s effectiveness as an Apple Board member will be significantly diminished, since he will have to recuse himself from even larger portions of our meetings due to potential conflicts of interest. Therefore, we have mutually decided that now is the right time for Eric to resign his position on Apple’s Board.”

This comes on the heels of Schmidt announcing he would "talk with Apple people", and on the controversial rejection of Google Voice and Google Latitude applications from the App Store, both now constrained to WebApp status on the iPhone and iPod touch.

Schmidt already recused himself from meetings involving the iPhone, which with 5.2 million sold last quarter and an platform install base in excess of 45 million, was increasingly core to Apple's business, even as Google began to explore the platform space themselves.

No word on who, if anyone, will replace him (though Apple's own chief operating officer, Tim Cook, has widely been rumored as a potential board member for a while now).