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We examine the onset of Anderson localization in three-dimensional systems with structural disorder in form of lattice irregularities and in the absence of any on-site disordered potential. Analyzing two models with distinct types of lattice regularities, we show that the Anderson localization transition occurs when the strength of the structural disorder is smoothly increased. Performing finite-size scaling analysis, we show that the transition belongs to the same universality class as regular Anderson localization induced by on-site disorder. Our paper identifies a class of structurally disordered lattice models in which destructive interference of matter waves may inhibit transport and lead to a transition between metallic and localized phases.