"What Amazon fears most: Diapers" declared the cover of BusinessWeek earlier this fall. Now it's clear that Amazon didn't fear diapers, it just wanted them for itself. Fortune has learned that Amazon.com on Monday will announce that it has agreed to acquire Quidsi, the parent company of websites like Diapers.com and Soap.com. The purchase price is $540 million in cash, with Quidsi's co-founders agreeing to multi-year employment contracts with Amazon (AMZN). The price tag is $200 million over what Quidsi was valued at in its latest round of venture financing.

    The site, launched in January 2005, was started by Marc Lore and Vinnie Bharara, who grew up together in New Jersey. A source says that this is not Amazon's first offer for their company, which had raised over $78 million in venture capital funding. The source says the company also received a (presumably lower) buyout offer from Wal Mart (WMT). (Messages left for Lore at home and to Bharara, Amazon PR, and Wal-Mart PR by email and phone weren't returned by time of posting.)

    So what do these giants want with a diaper and soap dispenser? A rapidly growing company with a devoted base of customers that has figured out how to warehouse and ship commodity items quickly and profitably. Another company with that same premise: Zappos.com, which Amazon snapped up for $1.1 billion in 2009.

    But it's not just about keeping customers. In a first-person account given to Inc. last year, Lore discussed the company's algorithmic approach to doing business:

    So before we launched, we built proprietary software from scratch. We built software with computational algorithms to determine what the optimal number of boxes to have in the warehouse is and what the sizes of those boxes should be. Should we stock five different kinds of boxes to ship product in? Twenty kinds? Fifty kinds? And what size should those boxes be? Right now, it's 23 box sizes, given what we sell, in order to minimize the cost of dunnage (those little plastic air-filled bags or peanuts), the cost of corrugated boxes, and the cost of shipping. We rerun the simulation every quarter. Using the right box probably adds close to 1 margin point.

    Sounds like the same kind of numbers-based approach to business practiced by the quant-trained Jeff Bezos.

    Quidsi shareholders include Accel Partners, Bessemer Venture Partners, BEV Capital, MentorTech Ventures and New Enterprise Associates.

    On a personal note, I'm writing this from the maternity ward at Brigham & Women's Hospital in Boston, where my daughter was born just a few days ago. I had no plans to do actual work here, but when the story is perfectly apropos...