We present a new method for computing NMR chemical shifts and magnetic susceptibilities in extended systems through an ab initio density functional perturbation theory approach. The method is applicable to crystalline and amorphous insulators under periodic boundary conditions, as well as to isolated molecules. The formalism exploits the exponentially decaying nature of localized Wannier orbitals. We have implemented the method in the context of a plane wave pseudopotential approach. The results are in good agreement with experiment and with calculations that use other theoretical methods.