Effective magnetic moments of drift Rydberg atoms in strong magnetic fields are obtained for different energy and angular-momentum states. Classical two-body trajectory calculations and quantum-mechanical one-body calculations are employed. For heavy atoms such as rubidium, the trapping dynamics can largely be explained by the net magnetic moment due to the cyclotron and the magnetron motion of the Rydberg electron. In light Rydberg atoms such as hydrogen, the intrinsic two-body nature of the dynamics becomes manifest in that the ionic motion significantly contributes to the effective magnetic moment. Also, light drift Rydberg atoms exhibit an anisotropic response to field-inhomogeneities parallel and transverse to the magnetic-field lines. The results are relevant to magnetic trapping of Rydberg atoms in strong-magnetic-field atom traps.