The Purkinje system is a heart structure responsible for transmitting electrical impulses through the ventricles in a fast and coordinated way to trigger mechanical contraction. Estimating a patient-specific compatible Purkinje Network from an electro-anatomical map is a challenging task, that could help to improve models for electrophysiology simulations or provide aid in therapy planning, such as radiofrequency ablation. In this study, we present a methodology to inversely estimate a Purkinje network from a patient's electro-anatomical map. First, we carry out a simulation study to assess the accuracy of the method for different synthetic Purkinje network morphologies and myocardial junction densities. Second, we estimate the Purkinje network from a set of 28 electro-anatomical maps from patients, obtaining an optimal conduction velocity in the Purkinje network of 1.95 ± 0.25 m/s, together with the location of their Purkinje-myocardial junctions, and Purkinje network structure. Our results showed an average local activation time error of 6.8±2.2 ms in the endocardium. Finally, using the personalized Purkinje network, we obtained correlations higher than 0.85 between simulated and clinical 12-lead ECGs.