We present a framework for quantization of electromagnetic field in the presence of dielectric media with time-varying optical properties. Considering a microscopic model for the dielectric as a collection of matter fields interacting with the electromagnetic environment, we allow for the possibility of dynamically varying light-matter coupling. We obtain the normal modes of the coupled light-matter degrees of freedom, showing that the corresponding creation and annihilation operators obey equal-time canonical commutation relations. We show that these normal modes can consequently couple to quantum emitters in the vicinity of dynamic dielectric media, and the resulting radiative properties of atoms are thus obtained. Our results are pertinent to time-varying boundary conditions realizable across a wide range of state-of-the-art physical platforms and timescales.