  We compute three-loop corrections to the relation between the heavy quark
masses defined in the pole and kinetic schemes. Using known relations between
the pole and $\overline{\rm MS}$ quark masses we can establish precise
relations between the kinetic and $\overline{\rm MS}$ charm and bottom masses.
As compared to two loops, the precision is improved by a factor two to three.
Our results constitute important ingredients for the precise determination of
the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ at Belle~II.
