Tensor-scalar theories of gravity are shown to generically contain an attractor mechanism toward general relativity, with the redshift at the beginning of the matter-dominated era providing the measure for the present level of deviation from general relativity. Quantitative estimates for the post-Newtonian parameters \ensuremath{\gamma}-1, \ensuremath{\beta}-1, and G\ifmmode \dot{}\else \.{}\fi{}/G are given, which give greater significance to future improvements of solar-system gravitational tests.