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Accurate numerical modeling of normal-conducting accelerator magnets requires a reliable characterization of the iron saturation and hysteresis as well as a precise knowledge of the magnet geometry as built. Computations of the field quality are not easily achieving the accuracy required by the accelerator operation, particularly for eddy-current effects in fast-ramping magnets. This paper proposes a (measurement) data-driven model for the nonlinear magnetization of normal-conducting magnets. The model adopts a volume integral formulation compatible with eddy-current simulations. A two-step updating procedure is applied. The first step is the fitting of material parameters directly in the magnet model. The second step is the updating of the magnetization by measurements of the integral field harmonics. The result is a full-order updated model that can be employed in static or dynamic simulations. Finally, the procedure is validated on an iron-dominated, normal-conducting magnet.