We develop an analytical approximate method for determining the Bohr radii of Wannier-Mott excitons in thin quantum wells under the influence of magnetic field perpendicular to the quantum well plane. Our hybrid variational-perturbative method allows us to obtain simple closed formulas for exciton binding energies and optical transition rates. We confirm the reliability of our method through exciton-polariton experiments realized in a GaAs/AlAs microcavity with an 8 nm In-x Ga1-xAs quantum well and magnetic field strengths as high as 14 T.