Earlier this week, the latest Steam Client Beta Update went live, adding the previously announced DualShock 4 support. As the patch notes show, downloading the beta update will give PlayStation 4 controllers access to the same sort of customization and configuration support as Steam Controllers:

Added Steam Configurator support for PS4 Dual Shock Controller. Note that this is a beta release. Enable in Big Picture settings Add/Test Controller settings. When enabled, PS4 controllers will have access to the same sort of customization/configuration support as Steam Controllers, including native API support.
PS4 Controllers using this system can map the trackpad, gyro, buttons, etc. to keyboard, mouse, or x-input outputs and can make use of action sets, touch menus, radial menus, and so forth. Added default PS4 templates.
Added software calibration for non-Steam controller based IMUs to counter for gyro drift.
Configuration Browser can now be toggled to show all available controller types rather than the default of the in-use controller type.
Configurations can now be marked as ?Unique? to a specific controller. This configuration will only be applied to that controller for that user?s account. By default, all controllers of a specific type will share a configuration unless marked as Unique.
Big Picture now supports PS4 controller glyphs when using Steam Configurator support.

When Steam launches Discovery Update 2.0 in the next couple of weeks, they’ll change their...