According to this Bloomberg report citing an anonymous source close to the "situation," the next Xbox (which is codenamed "Durango" or is currently being called the Xbox 720) will not be backwards compatible with current generation Xbox 360 discs. Other rumors have indicated that the system will be pretty expensive - reaching the price point of close to $500 for the premium model of the system, though a cheaper model will also be available.
Bloomberg says that the new system will use the AMD "Jaguar" chip - the same AMD system-on-a-chip that will be utilized in the PlayStation 4. Because the game discs made for the Xbox 360 are reliant on the system's IBM PowerPC CPU, they won't be compatible with the new system, according to the source.
Rumors indicate that Microsoft is planning an Xbox event in May, though Microsoft has yet to confirm this story, nor has it spoken about today's news quite yet. The company also wouldn't confirm or deny if its new system will require a constant internet connection in order to play games.