A sterilization apparatus (1) for sterilizing objects, said sterilization apparatus (1) comprising: a chamber (2) for receiving said objects to be sterilized, said chamber (2) having an inlet of the sterilization means (3a) and an outlet of the sterilization medium (3b); an inlet flow control device (14) connected to said inlet of the sterilization means (3a) to control a supply of a sterilization means to said chamber (2); a drainage system (6) connected to said outlet of the sterilization means (3b) of the chamber (2) for the controllable discharge of fluid from said chamber (2); and a control unit (12) connected to said inlet flow control device (14) and to said drainage system (6) and configured to control said inlet flow control device (14) and said drainage system ( 6) according to a predefined sterilization scheme; characterized in that the drainage system (6) comprises: a drainage inlet (60) connected to said outlet of the sterilization means (3b) of the chamber (2); a drain outlet (62) connected to a vacuum system (8) for the evacuation of the chamber (2); a first conduit (64) connecting said drain inlet (60) and said drain outlet (62); and a proportional valve (66) disposed along said first conduit (64), said proportional valve (66) being controllable by said control unit (12) to partially restrict the flow of fluid through said first conduit (64 ) in accordance with a predefined continuous relationship between a control parameter and a valve opening of said proportional valve (66).Un aparato de esterilización (1) para esterilizar objetos, comprendiendo dicho aparato de esterilización (1): una cámara (2) para recibir dichos objetos a esterilizar, teniendo dicha cámara (2) una entrada del medio de esterilización (3a) y una salida del medio de esterilización (3b); un dispositivo de control de flujo de entrada (14) conectado a dicha entrada del medio de esterilización (3a) para controlar un suministro de un medio de esterilización a dicha cámara (2); un siste