From what I remember, How to Open a Chess Game had a chapter on it written by Petrosian himself.  I would use the Classical King's Indian book by Everyman.  It has great up-to-date coverage on everything.  It's really a must-buy IMO.

Seconding Palliser's Play 1 d4! (although I think it may be out of print). And as with any KID question, if you can track down a copy of Bellin and Ponzetto's Mastering the King's Indian, snatch it up immediately.

Gallagher's Starting Out: King's Indian is mostly targeted at Black players, but contains good explanations of White's plans in every major variation, including the Petrosian.

The games of Petrosian himself should be a good start. I heard there is actually a book dedicated to his treatment of the King's Indian, but only in Russian.

I have "Tigran Petrosjan: Die Karriere eines Schachgeines" by his second Suetin, but the notes in it are often brief and there are no doubt better books out there.

Also be sure to look at Kramnik's games with it from the early/mid 90s, I think he even beat Kasparov with it. It always helps to have a good idea what you want to achieve with White.

A lot of the theoretical material out there on the Petrosian is written with Black players in mind. Apart from Palliser, "The Classical King's Indian Uncovered" by Panczyk/Ilczuk attempted objective coverage. ChessPublishing should have some coverage too, though the line hasn't been theoretically 'hot' for many years.

Any suggestions for learning the Petrosian KID as White - books, DVDs, anything. I have no experience with the KID at all (play Torre Attack now) and I've chosen the Petrosian as a first step in taking on the KID, so I need something that gives me some idea of how to play the KID in general and this line in particular.