We study gluodynamics in an external Abelian electromagnetic field within the dual superconductor approach. We show that the SU(2) gluodynamics should possess a deconfining phase transition at zero temperature at certain value of the external field. A dual superconductor model for the SU(3) gauge theory in external field predicts a rich phase structure containing confinement, asymmetric confinement and deconfinement phases. These results can be used to check the validity of the dual superconductor description of gluodynamics in external fields. We also discuss the gauge-independence of the obtained results.