We derive the relativistic formulas for the van der Waals coefficients of Yb-alkali-metal dimers that correlate to ground and excited separated-atom limits. We calculate C-6 and C-8 coefficients of particular experimental interest. We also derive a semiempirical formula that expresses the C-8 coefficient of heteronuclear A + B dimers in terms of the C-6 and C-8 coefficients of homonuclear dimers and the static dipole and quadrupole polarizabilities of the atomic states A and B. We report results of calculation of the C-6 coefficients for the Yb-Rb P-3(1)0 + 5s S-2(1/2) and S-1(0) + (5)p P-2(1/2)0 dimers, and the C-8 coefficients for the Yb-Li S-1(0) + 2s S-2(1/2) and Yb-Rb S-1(0) + 5s S-2(1/2) dimers. Uncertainties are estimated for all predicted properties.