A vehicle braking system includes a controller that receives signals from sensors associated with vehicle disc brakes, which allow detection of a parameter indicative of a degree of noise generated from each disc brake. When noise generation is detected, the controller activates a noise attenuation function of a first type if the vehicle is braking, and of a second type if the vehicle is not braking. The first type involves reducing actuating pressure of a fluid actuator associated with the disc brake for which noise generation is detected. The second type involves temporarily activating, while the vehicle is running and not braking, the fluid actuator associated with the disc brake which is generating noise. The controller also receives signals indicative of vehicle operating parameters which allow conditions to be defined in which priority is given to vehicle safety, and in which the noise attenuation function is excluded.