In this manuscript we present a true pulse-on-demand concept of a hybrid CPA laser system, consisting of a chirped-pulse fiber amplifier and an additional solid-state amplifier, capable of generating femtosecond pulses on demand without an external optical modulator/shutter. Pulse-on-demand operation is achieved by introducing idler pulses with a few nanoseconds duration and selectively switching between the femtosecond and idler pulses. The idler pulses are used to maintain a constant population inversion in the fiber amplifier as well as in the solid-state amplifier. Second harmonic generation (SHG) unit then effectively filters out the idler pulses due to their low peak power, leaving only a stable femtosecond pulse train. This concept is demonstrated on a CPA hybrid system that can generate pulses with up to 200 µJ at 515 nm with a pulse duration under 450 fs. As there is no optical modulator at the laser output, the presented concept also enables further power scaling.