Using molecular dynamics simulations performed with the TIP4P and SPC/E pair potentials we examine the process of field-induced crystallization (electro freezing) of supercooled liquid water. In the presence of an electric field the transformation of a liquid into a crystalline solid is observed for a narrow range of density and temperature on a time scale of a few hundred picoseconds. The resulting crystal has the structure of polar cubic ice I. TIP4P water appears to be more susceptible to nucleation than SPC/E water. For a field of 0.5 V/Angstrom TIP4P water undergoes crystallization at densities between 0.94 and 0.96 g/cm(3) at a temperature of 250 K. Intermediate structures emerging during the electrofeeezing of water closely resemble a low-density amorphous ice. We observe formation of a high-density amorphous component at densities above those favoring the crystallization of the cubic ice. Application of an electric field to low-density water samples (0.90-0.92 g/cm(3) for TIP4P water at 250 K) produces low-density amorphous ices. Constant density conditions were found to be more favorable than constant pressure conditions for producing polar ice crystals.