An assembly of a MEMS integrated device envisages: a package having a base substrate with a main surface in a horizontal plane, and a coating set on the base substrate; a first body including semiconductor material and integrating a micromechanical structure, housed within the package on the base substrate; at least one second body including semiconductor material and integrating at least one electronic component, designed to be functionally coupled to the micromechanical structure, the first body and the second body being arranged within the package stacked in a vertical direction transverse to the horizontal plane. In particular, at least one between the first body and the base substrate defines a first recess, in which the second body is housed, at least in part.