Sprint announces Moto X coming this summer for $19929
So far, no carrier has given a specific date, and Sprint doesn't seem to want to jump the gun in that regard either. In its official announcement for the X, Sprint simply says that the device will launch "this summer". And since Motorola already said the device would be launching later this month or possibly in early September on some carriers, a frame of "this summer" doesn't help to narrow down the window at all.
The device will run on Sprint's growing LTE network, which currently only reaches 151 markets around the U.S. If you want more info on the Sprint release, you can sign up on the carrier's info page for the X.