Since the 1920s, the Enskog solutions to the Boltzmann equation have provided a route to predicting the transport properties of dilute gas mixtures. At higher densities, predictions have been limited to gases of hard spheres. In this work, we present a revised Enskog theory for multicomponent mixtures of Mie fluids, where the Barker-Henderson perturbation theory is used to calculate the radial distribution function at contact. With parameters of the Mie-potentials regressed to equilibrium properties, the theory is fully predictive for transport properties. The presented framework offers a link between the Mie potential and transport properties at elevated densities, giving accurate predictions for real fluids. For mixtures of noble gases, diffusion coefficients from experiments are reproduced within ±4%. For hydrogen, the predicted self-diffusion coefficient is within 10% of experimental data up to 200 MPa and at temperatures above 171 K. Binary diffusion coefficients of the CO2/CH4 mixture from simulations are reproduced within 20% at pressures up to 14.7 MPa. Except for xenon in the vicinity of the critical point, the thermal conductivity of noble gases and their mixtures is reproduced within 10% of the experimental data. For other molecules than noble gases, the temperature dependence of the thermal conductivity is under-predicted, while the density dependence appears to be correctly predicted. Predictions of the viscosity are within ±10% of the experimental data for methane, nitrogen, and argon up to 300 bar, for temperatures ranging from 233 to 523 K. At pressures up to 500 bar and temperatures from 200 to 800 K, the predictions are within ±15% of the most accurate correlation for the viscosity of air. Comparing the theory to an extensive set of measurements of thermal diffusion ratios, we find that 49% of the model predictions are within ±20% of the reported measurements. The predicted thermal diffusion factor differs by less than 15% from the simulation results of Lennard-Jones mixtures, even at densities well exceeding the critical density.