We demonstrate digital tuning of the slow-light regime in silicon photonic-crystal waveguides by performing atomic layer deposition of hafnium oxide. The high group-index regime was deterministically controlled (redshift of 140±10 pm per atomic layer) without affecting the group-velocity dispersion and third-order dispersion. Additionally, differential tuning of 110±30 pm per monolayer of the slow-light TE-like and TM-like modes was observed. This passive postfabrication process has potential applications including the tuning of chip-scale optical interconnects, as well as Raman and parametric amplification.