The transition from diffusive transport to localization of waves should occur for any type of classical or quantum wave in any media as long as the wavelength becomes comparable to the transport mean free path l*. The signatures of localization and those of absorption, or bound states, can, however, be similar, such that an unequivocal proof of the existence of wave localization in disordered bulk materials is still lacking. Here we present time resolved measurements of light transport through strongly scattering samples with kl* values as low as 2.5. In transmission, we observe deviations from diffusion which cannot be explained by absorption, sample geometry, or reduction in transport velocity. Furthermore, the deviations from classical diffusion increase strongly with decreasing l* as expected for a phase transition. This constitutes an experimental realization of the critical regime in the approach to Anderson localization.