We study the magnetic susceptibility x of a two-dimensional noninteracting electron gas confined by a smooth chaotic potential. The computation of x for a wide range of magnetic field values B reveals that the chaotic (B50) to regular (B ! `) transition is dominated by bifurcations of short periodic orbits that become stable as B increases. The families of stable orbits and tori contained in the associated stability islands do not play any special role in this regime. Large contributions, however, are observed near the bifurcation points, increasing the average susceptibility to values beyond those expected for regular systems.