We extend the application of the mode-coupling theory for the dynamics of critical fluctuations in fluids into the non-asymptotic critical region. An approximate solution bf the mode-coupling equations yields a set of representative equations for the thermal conductivity and the viscosity of one-component fluids which incorporates the crossover from asymptotic singular behavior near the critical point to the regular behavior of these transport properties far away from the critical point. The equations for the critical enhancements of the thermal conductivity and the viscosity depend on the background transport properties of the fluid, the equilibrium thermodynamic properties of the fluid, and one fluid-dependent wave-number cutoff q(D), which is indicative of the crossover length scale. We compare our crossover model with experimental data for the thermal diffusivity, the thermal conductivity, and the viscosity of carbon dioxide and ethane.