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Abstract We investigate electrical charge transport in hot magnetized plasma using first-principles quantum field theoretical methods. By employing Kubo’s linear response theory, we express the electrical conductivity tensor in terms of the fermion damping rate in the Landau-level representation. Utilizing leading-order results for the damping rates from a recent study within a gauge theory, we derive the transverse and longitudinal conductivities for a strongly magnetized plasma. The analytical expressions reveal drastically different mechanisms that explain the high anisotropy of charge transport in a magnetized plasma. Specifically, the transverse conductivity is suppressed, while the longitudinal conductivity is enhanced by a strong magnetic field. As in the case of zero magnetic field, longitudinal conduction is determined by the probability of charge carriers to remain in their quantum states without damping. In contrast, transverse conduction critically relies on quantum transitions between Landau levels, effectively lifting charge trapping in localized Landau orbits. We examine the temperature and magnetic field dependence of the transverse and longitudinal electrical conductivities over a wide range of parameters and investigate the effects of a nonzero chemical potential. Additionally, we extend our analysis to strongly coupled quark-gluon plasma and study the impact of the coupling constant on the anisotropy of electrical charge transport.