The perpendicular critical fields of a superconducting film have been strongly enhanced by using a nanoengineered lattice of magnetic dots (dipoles) on top of the film. Magnetic-field-induced superconductivity is observed in these hybrid superconductor / ferromagnet systems due to the compensation of the applied field between the dots by the stray field of the dipole array. By switching between different magnetic states of the nanoengineered field compensator, the critical parameters of the superconductor can be effectively controlled. When the applied magnetic field exceeds a certain critical value, superconductivity is suppressed due to orbital and spin pair breaking effects. This very general property of superconductors sets strong limits for their practical applications, since, in addition to applied magnetic fields, the current sent through a superconductor also generates magnetic fields, which can lead to a loss of zero resistance. Materials that are not only able to withstand magnetic fields, but in which superconductivity can even be induced by applying a magnetic field, are very rare and up to now only (EuSn)Mo 6 S 8 [1, 2], organic λ-(BETS) 2 FeCl 4 materials [4,5] and HoMo 6 S 8 [3] show this unusual behavior. The appearance of magnetic-fieldinduced superconductivity (FIS) in the former two compounds was interpreted in terms of the Jaccarino-Peter effect [6], in which the exchange fields from the paramagnetic ions compensate an applied magnetic field, so that the destructive action of the field is neutralized. Here we report that FIS can also be realized in hybrid superconductor / ferromagnet nanostructured bilayers. The basic idea is quite straightforward (see Fig. 1): a lattice of magnetic dots with magnetic moments aligned along the positive z-direction is placed on top of a superconducting film. The magnetic stray field of each dot has a positive z-component of the magnetic induction B z under the dots and a negative one in the area between the dots. Added to a homogeneous magnetic field H, see Fig. 1(b), these dipole fields enhance the z-component of the effective magnetic field µ 0 H ef f = µ 0 H + B z in the small area just under the dots and, at the expense of that, reduce H ef f everywhere else in the Pb film, thus providing the condition necessary for the FIS observation. This new field compensation effect is not restricted to specific superconductors, so that FIS could be achieved in any superconducting film with a lattice of magnetic dots. To implement the idea of the nanoengineered FIS, we have prepared a sample, which reminds us of other systems used during the last decade for studying flux pinning by periodic arrays of magnetic dots