We provide global models of line-driven winds of B supergiants for metallicities corresponding to the Large and Small Magellanic Clouds. The velocity and density structure of the models is determined consistently from hydrodynamical equations with radiative force derived in the comoving frame and level populations computed from kinetic equilibrium equations. We provide a formula expressing the predicted mass-loss rates in terms of stellar luminosity, effective temperature, and metallicity. Predicted wind mass-loss rates decrease with decreasing metallicity as Ṁ ∼ Z^0.60 and are proportional to the stellar luminosity. The mass-loss rates increase below the region of the bistability jump at about 20 kK because of iron recombination. In agreement with previous theoretical and observational studies, we find a smooth change of wind properties in the region of the bistability jump. With decreasing metallicity, the bistability jump becomes weaker and shifts to lower effective temperatures. At lower metallicities above the bistability jump, our predictions provide similar rates to those used in current evolutionary models, but our rates are significantly lower than older predictions below the bistability jump. Our predicted mass-loss rates agree with observational estimates derived from Hα line assuming that observations of stellar winds from Galaxy and the Magellanic Clouds are uniformly affected by clumping. The models nicely reproduce the dependence of terminal velocities on temperature derived from ultraviolet spectroscopy.