An analog soft-start circuit for a switching regulator (e.g., a buck converter) including an analog ramp circuit and an open-loop analog voltage clamp circuit. The voltage ramp circuit utilizes a two-stage current divider circuit to generate a very low, stable current signal, and an integrator circuit including a relatively small, integral capacitor to generate the ramp voltage signal in response to the very low current signal. The analog voltage clamp circuit clamps the regulated output signal to the ramp voltage until the ramp voltage signal increases to a predetermined voltage level, thereby causing the regulated output voltage to exhibit the desired soft-start characteristics. The analog clamp circuit includes a current mirror circuit that generates a clamp current that pulls down the error amplifier output stage via a clamping element (e.g., a diode) until the ramp voltage signal reaches a predetermined level.