The study of hot plasma expansion in a magnetic field is of interest for many laboratory and astrophysical applications. In this paper, an exactly solvable analytical model is proposed for an expanding resistive plasma in an external magnetic field in the regime in which the magnetic field does not perturb the plasma motion. The model is based on a class of exact solutions for the purely radial expansion of the plasma in the absence of a magnetic field. This approximation permits the reduction of the electromagnetic problem to consideration of a diffusion equation for the magnetic field. Explicit solutions are derived for a resistive cylindrical plasma expanding into a uniform ambient magnetic field. Some numerical examples related to the laser-produced plasma experiments are presented.