A method of manufacturing a transducer module (10; 40), comprising the steps of: - forming, on a substrate , a first MEMS transducer subjected, in use, to a first environmental stimulus and configured to generate a first transduced signal as a function of the first environmental stimulus; - forming, on the substrate , a second MEMS transducer having a membrane suspended over the substrate , configured to detect an environmental quantity and generate a second transduced signal as a function of the environmental quantity detected; - forming, on the substrate , a conductive layer ; and - defining the conductive layer to form, at the same time, said membrane of the second MEMS transducer and at least one conductive strip (4c; 4d) electrically coupled to the first MEMS transducer , wherein the step of forming the first MEMS transducer includes forming an inertial sensor and the step of forming the second MEMS transducer includes forming a pressure sensor, characterized in that the method further comprises the steps of:- coupling a cap , having a first recess, on the substrate so as to form a first chamber that houses the first and second MEMS transducers ; - forming in the first chamber a getter element configured to generate, when activated, an internal pressure (P1) in the first chamber ; - forming at least one hole extending throughout the thickness of the substrate as far as the membrane , so that the membrane has a first surface facing the inside of the first chamber and a second surface, opposite to the first surface, facing an environment outside the first chamber through said at least one hole ; - activating the getter element to generate said internal pressure (P1) within the first chamber such that, during use, said membrane undergoes deformation according to a difference between the internal pressure (P1) and a pressure (P2) of the environment outside the first chamber . - forming, on a substrate , a first MEMS transducer subjected, in use, to a first environmental stimulus and configured to generate a first transduced signal as a function of the first environmental stimulus; - forming, on the substrate , a second MEMS transducer having a membrane suspended over the substrate , configured to detect an environmental quantity and generate a second transduced signal as a function of the environmental quantity detected; - forming, on the substrate , a conductive layer ; and - defining the conductive layer to form, at the same time, said membrane of the second MEMS transducer and at least one conductive strip (4c; 4d) electrically coupled to the first MEMS transducer , - forming in the first chamber a getter element configured to generate, when activated, an internal pressure (P1) in the first chamber ; - forming at least one hole extending throughout the thickness of the substrate as far as the membrane , so that the membrane has a first surface facing the inside of the first chamber and a second surface, opposite to the first surface, facing an environment outside the first chamber through said at least one hole ; - activating the getter element to generate said internal pressure (P1) within the first chamber such that, during use, said membrane undergoes deformation according to a difference between the internal pressure (P1) and a pressure (P2) of the environment outside the first chamber . <EOS>