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 (20, 30); - forming in the first chamber a getter element configured to generate, when activated, an internal pressure 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 within the first chamber such that, during use, said membrane undergoes deformation according to a difference between the internal pressure and a pressure 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 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 within the first chamber such that, during use, said membrane undergoes deformation according to a difference between the internal pressure and a pressure of the environment outside the first chamber.