Online retailer Amazon has just acquired the company that makes Stanza, the popular eBook reader for the iPhone.

Stanza is the perfect complement for Amazon’s Kindle, the eBook reading device. The Kindle itself has been released as an application for the iPhone. That application, called Kindle for the iPhone, is now the No. 1 ebook application for the iPhone. But here’s why it doesn’t overlap with Stanza. First, to really appreciate the Kindle app, you had to shell out $359 for the Kindle. Then the app, available for free in the App Store, gives you access to all the eBooks you can find in the Kindle store. It’s not perfect — you need to buy the books on the web for example, and then they get transferred over to your Kindle app.

But Stanza gives users ebook downloads for free, via a free iPhone app that is completely standalone. To be sure, the Kindle for the iPhone is immensely popular. It only recently surpassed Stanza, which had earlier been the most popular, and which had impressed us in our review. Stanza clearly caught Amazon’s attention last year, after Stanza was downloaded 200,000 times — compare Amazon Kindle’s sales of 40,000 units per month, before the Kindle App was launched last month. And regardless of whether you’re a Stanza partisan (like VentureBeat’s Anthony Ha), a Kindle fan, or both, there’s clearly a hunger for reading on the iPhone.

ReadWriteWeb just reported the deal, noting that neither Stanza nor Amazon disclosed the price of the acquisition.

Stanza, which is free, offers downloads of older works that have entered the public domain (in other words, no one owns the copyright), from places such as Project Gutenberg and Feedbooks, available through a Creative Commons license, as well as about 50,000 titles from partners such as Fictionwise eReader store (which is now owned by Barnes and Noble) and O’Reilly.

According to Lexcycle, the company that owns Stanza, and which is being bought by Amazon, there are no plans yet to change the Stanza app or user experience because of this acquisition. Lexcycle will continue its relationships with its content partners.

Stanza has been a proponent of open eBook standards like EPUB, RWW notes, while Amazon has always kept its system relatively closed. Lexcycle announced recently that it was working together with Adobe to develop an open standard for eBook catalogs.