By performing high-resolution two-color photoassociation spectroscopy, we have successfully determined the binding energies of several of the last bound states of the homonuclear dimers of six different isotopes of ytterbium. These spectroscopic data are in excellent agreement with theoretical calculations based on a simple model potential, which very precisely predicts the s-wave scattering lengths of all 28 pairs of the seven stable isotopes. The s-wave scattering lengths for collision of two atoms of the same isotopic species are 13.33(18) nm for Yb-168, 3.38(11) nm for Yb-170, -0.15(19) nm for Yb-171, -31.7(3.4) nm for Yb-172, 10.55(11) nm for Yb-173, 5.55(8) nm for Yb-174, and -1.28(23) nm for Yb-176. The coefficient of the lead term of the long-range van der Waals potential of the Yb-2 molecule is C-6=1932(30) atomic units (E(h)a(0)(6)approximate to 9.573x10(-26) J nm(6)).