We systematically develop the full quantum theory for the electromagnetic induced transparency (EIT) and slow light properties in ultracold Bose and Fermi gases. It shows a very different property from the classical theory which assumes frozen atomic motion. For example, the speed of light inside the atomic gases can be changed dramatically near the Bose-Einstein condensation temperature, while the presence of the Fermi sea can destroy the EIT effect even at zero temperature. From experimental point of view, such quantum EIT property is mostly manifested in the counter-propagating excitation schemes in either the low-lying Rydberg transition with a narrow line width or in the D2 transitions with a very weak coupling field. We further investigate the interaction effects on the EIT for a weakly interacting Bose-Einstein condensate, showing an inhomogeneous broadening of the EIT profile and nontrivial change of the light speed due to the quantum many-body effects beyond mean field energy shifts.