By now it is known that in a singlet superconductor-ferromagnet (S-F) structure the superconducting correlations carried by opposite-spin pairs penetrate into the ferromagnet over a short distance of the order of magnetic coherence length. The long-range proximity effect (LRPE), taking place on the length scale of the normal metal coherence length, can only be maintained by equal-spin pairs, which can be generated by magnetic inhomogeneities in the system. In this Letter, we have predicted a new type of LRPE, which can take place in S-F heterostructures under nonequilibrium conditions. The superconducting correlations in the F region are generated by opposite-spin Cooper pairs and equal-spin pairs are not involved. The possibility for an opposite-spin pair to penetrate into the ferromagnet over a large distance is provided by creation of the proper nonequilibrium quasiparticle distribution there. This leads to a sharp increase (up to a few orders of magnitude) of the critical Josephson current through a S-F-S junction at some values of the voltage controlling the nonequilibrium distribution in the F interlayer.