A multiferroic material has been synthesized by first growing BaTiO(3) nanocrystals in a silica glass and then subjecting the composite to a two-stage ion-exchange reaction of the type Ti(4+) <-> 2Ni(2+). The nanocomposite retained the usual ferroelectric characteristics with lower values of the dielectric constant and remanent polarization. It also showed ferromagnetic hysteresis at temperatures in the range 10-300 K. At temperatures below similar to 10 K, the magnetization exhibited a sharp increase as the temperature was reduced. This has been explained on the basis of a one-dimensional Heisenberg ferromagnet consisting of Ni(2+) ions at the surfaces of the nanocrystals. The nanocomposite showed magnetodielectric coupling at room temperature. The dielectric constant increased as a function of magnetic field, showing a maximum at 4 kOe. This has been ascribed to magnetostriction of the new BaTiO(3) nanocrystalline phase.