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 14010 pm per atomic layer without affecting the group-velocity dispersion and third-order dispersion. Additionally, differential tuning of 11030 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.