The release date has unfortunately not been revealed other than for a vague suggestion that it will be coming this Summer.
Considering that Motorola has stated that the device is coming later this month or early next month on some carriers. We cant really estimate an exact date for the device.
The device will run on Sprint's growing LTE network, which currently only reaches 151 markets around the U.S. and if you are interested in choosing Sprint as your carrier you can pre-register for your Moto X on Sprint right now. You can learn more about the Motorola Moto X here.
source - Sprint