In recent years, metal halide perovskites have generated tremendous interest for optoelectronic applications and their underlying fundamental properties. Because of the large electron-phonon coupling characteristic of soft lattices, self-trapping phenomena are expected to dominate hybrid perovskite photoexcitation dynamics. Yet, while the photogeneration of small polarons was proven in low-dimensional perovskites, the nature of polaron excitations in technologically relevant 3D perovskites, and their influence on charge carrier transport, remain elusive. In this study, we used a combination of first principle calculations and advanced spectroscopy techniques spanning the entire optical frequency range to pin down polaron features in three-dimensional metal halide perovskites. Mid-infrared photoinduced absorption shows the photogeneration of states associated with low energy intragap electronic transitions with lifetime up to the millisecond time scale, and vibrational mode renormalization in both frequency and amplitude. Density functional theory supports the assignment of the spectroscopic features to large polarons leading to new intragap transitions, hardening of phonon mode frequency, and renormalization of the oscillator strength. Theory provides quantitative estimation for the charge carrier masses and mobilities increase upon polaron formation, confirming experimental results. Overall, this work contributes to complete the scenario of elementary photoexcitations in metal halide perovskites and highlights the importance of polaronic transport in perovskite-based optoelectronic devices.