In this work, we generate curved Lorentzian manifolds from a flat Minkowskian space-time, through the Gravitational Decoupling by the Minimal Geometric Deformation method interpreting the decoupling sector as a generator of curvature and matter distribution. In particular, we obtain some new wormhole geometries by imposing either physically relevant equations of state or certain physically-motivated geometric constraints. These solutions are analyzed in detail. For all these solutions, we study the associated energy conditions, the geometric behavior and construct their embedding diagrams.