The dynamical localization of non-Abelian gauge fields in non-compact flat D dimensions is worked out. The localization takes place via a field-dependent gauge kinetic term when a field condenses in a finite region of spacetime. Such a situation typically arises in the presence of topological solitons. We construct a 4D low-energy effective Lagrangian up to the quadratic order in a universal manner applicable to any spacetime dimensions. We devise an extension of the R_xi gauge to separate physical and unphysical modes clearly. Out of the D-dimensional non-Abelian gauge fields, the physical massless modes reside only in the 4D components, whereas they are absent in the extra-dimensional components. The universality of non-Abelian gauge charges holds due to the unbroken 4D gauge invariance. We illustrate our methods with models in D = 5 (domain walls), D = 6 (vortices), and D = 7.