We present an algorithm for the linear inversion of two-dimensional (2-D) surface magnetic data to obtain 3-D models of the susceptibility of the source. The forward model is discretized by a mesh of prismatic cells with constant magnetization that allows the recovery of a complete 3-D generating source. As the number of cells are normally greater than the amount of available data, we have to solve an underdetermined linear inverse problem. A Tikhonov regularization of the solution is introduced as a depth-weighting function adapted from Li and Oldenburg (1996) to close the source toward the bottom. The main novelty of this method is a first-stage optimization that gives information about the depth to the bottom of the generating source. This parameter permits both the evaluation of the appropriate vertical extension of the mesh and the definition of the shape of the regularizing depth-weighting distribution. After discussing the performance of this method by showing the results of various synthetic tests, we invert the magnetic anomalies of the volcanic edifices in the Latium region in central Italy to define their 3-D source distribution.