In an assembly of modules with magnetic anchorage for the construction of a grid structure, a joining element for connecting rigidly at least a first and a second elongated modules of the grid structure, characterised in that it comprises: a body of the joining element; at least a first and a second tubular projections of the body for axial attachment of the first and respectively second elongated modules; and a housing of the body for securing the body to a further module of the grid structure; the at least first and second tubular projections being in direct communication with the housing for contact of the further module to the at least first and second elongated modules.