The theory of spin fluctuations is developed for an ensemble of localized electrons, taking into account both the hyperfine interaction of electron and nuclear spins and electron hopping between the sites. The analytical expression for the spin noise spectrum is derived for an arbitrary relation between the electron spin precession frequency in a field of nuclear fluctuations and the hopping rate. An increase in the hopping rate results in a drastic change in the spin noise spectrum. The effect of an external magnetic field is briefly addressed.