We present an inversion methodology for defect characterization using the data from magnetic flux leakage (MFL) measurements. We use a single tangential component of the leakage field as the MFL response. The inversion procedure employs the space mapping methodology. Space mapping is an efficient technique that shifts the optimization burden from a computationally expensive accurate (fine) model to a less accurate (coarse) but fast model. Here the fine model is a finite-element method (FEM) simulation, while the coarse model is based on analytical formulas. We achieve good estimation of the defect parameters using just a few FEM simulations, which leads to substantial savings in computational cost as compared to other optimization approaches. We examine the efficiency of the proposed inversion technique in estimating the shape parameters of rectangular and cylindrical defects in steel pipes. Our results show good agreement between the actual and estimated defect parameters.