We demonstrate nonlinear compression of pulses at 1.03 µm and repetition rate of 200 kHz generated by a ytterbium fiber laser using two cascaded all-solid-state multipass cells. The pulse duration has been compressed from 460 to 22 fs, corresponding to a compression factor of ∼21. The compressed pulse energy is 15.6 µJ, corresponding to an average power of 3.1 W, and the overall transmission of the two compression stages is 76%. The output beam quality factor is M² ∼1.2 and the excess intensity noise introduced by nonlinear broadening is below 0.05%. These results show that nonlinear pulse compression down to ultrashort durations can be achieved with an all-solid-state approach, at pulse energies much higher than previously reported, while preserving the spatial characteristics of the laser.