It's about time.
This will save Amazon Billions of dollars in shipping per year. Yes, that's Billions with a B. In 2012 they spent over 5 billion dollars just in shipping fees to send stuff to customers, and that's at a steeply discounted rate from their shipping suppliers.
If they can put just a few thousand drones on each warehouse, working during daylight hours they could easily drop a few billion in shipping costs.
It's still awhile away, though, because the FAA does not yet allow civilian or commercial drone operation. They allow radio control flights, but they must be within an operator's line of sight at all times. Some people and businesses are skirting this law, and a few of them are getting caught (mostly for doing it stupidly, or advertising their service and having competitor's tattletaling on them to regulators).
There are other risks associated with such a program, but the benefits will certainly outweigh the risks for a business as large as Amazon.
In fact, I expect others to clamor to it as well - walmart, cosco, mcdonalds, pizza hut, etc will certainly try to implement such a system. We're going to have a bumpy ride as the FAA and regulators figure out how to implement autonomous drone laws (and they'll have to be autonomous - with one operator managing a few dozen in flight at any given time), but it'll come.
Probably a prime time to start a drone company, actually. There are hundreds already starting, but what is really needed is a lobbying effort to guide the regulators in a good direction that doesn't lead to problems.