An electroacoustic MEMS transducer, having a substrate of semiconductor material; a through cavity in the substrate; a back plate carried by the substrate through a plate anchoring structure, the back plate having a surface facing the through cavity; a fixed electrode, extending over the surface of the back plate; a membrane of conductive material, having a central portion facing the fixed electrode and a peripheral portion fixed to the surface of the back plate through a membrane anchoring structure; and a chamber between the membrane and the back plate, peripherally delimited by the membrane anchoring structure.