Apparently, Sprint has already been field testing and installing 4G LTE equipment in several parts of their network, and they plan on beginning the LTE rollout starting early next year. In fact, Sprint plans to launch the service for customers as early as the first or second quarter of 2012.

Interestingly, the costs for this upgrade where already factored into their financial report, so it won't require any additional capital investment. This means that very soon next year, Sprint will have another attractive selling point beyond just their cheaper pricing and unlimited data plans, and will become even more competitive.

This was not an official announcement, but that is expected to take place on October 7th. Dan Hesse, Sprint's CEO, said to investors during a conference hosted by Goldman Sachs last week, "On October 7, we're focusing on Sprint and our network." Sprint plans to continue supporting WiMax, which will simply give them broader options. Here's a quote from the CNET article with some additional info,
The 4G component is part of Sprint's grand Network Vision plan, which represents a massive overhaul of its entire network infrastructure. The project, which is expected to cost $4 billion to $5 billion over the next three to five years, will swap in new equipment that can run multiple wireless technologies, from its 3G CDMA network to LTE.

The $4 billion to $5 billion estimate, which will be doled out to vendors L.M. Ericsson, Alcatel-Lucent, and Samsung Electronics, also includes its 4G deployment.

Sprint has said that the project will save the company between $10 billion and $11 billion over a seven-year period.
Source: CNET