Post-compression methods for ultrafast laser pulses typically face challenging limitations, including saturation effects and temporal pulse breakup, when large compression factors and broad bandwidths are targeted. To overcome these limitations, we exploit direct dispersion control in a gas-filled multi-pass cell, enabling, for the first time to the best of our knowledge, single-stage post-compression of 150 fs pulses and up to 250 µJ pulse energy from an ytterbium (Yb) fiber laser down to sub-20 fs. Dispersion-engineered dielectric cavity mirrors are used to achieve nonlinear spectral broadening dominated by self-phase modulation over large compression factors and bandwidths at 98% throughput. Our method opens a route toward single-stage post-compression of Yb lasers into the few-cycle regime.