FromSoftware and Bandai Namco have posted the official minimum and recommended PC specifications on Dark Soul III's Steam page. The minimum specs seem to call for at least a first generation Llano based APU combined with a first generation low-end GPU.
Dark Souls III is set to release on April 12th 2016, which isn't as far off as it sounds.
Minimum specs
OS: Windows 7 SP1 64bit, Windows 8.1 64bit Windows 10 64bitProcessor: AMD A8 3870 3.6 Ghz or Intel Core i3 2100 3.1GhzMemory: 8 GB RAMGraphics: NVIDIA GeForce GTX 465 / ATI Radeon HD 6870DirectX: Version 11Network: Broadband Internet connectionStorage: 50 GB available spaceSound Card: DirectX 11 sound deviceRecommended specs
OS: Windows 7 SP1 64bit, Windows 8.1 64bit Windows 10 64bitProcessor: AMD FX 8150 3.6 GHz or Intel Core™ i7 2600 3.4 GHzMemory: 8 GB RAMGraphics: NVIDIA GeForce GTX 750, ATI Radeon HD 7850DirectX: Version 11Network: Broadband Internet connectionStorage: 50 GB available space