Density turbulence suppression is observed in the Internal Transport Barrier (ITB) region of JET discharges with optimised magnetic shear. The suppression occurs in two stages. First, low frequency turbulence is reduced across the plasma core by a toroidal velocity shear generated by intense auxiliary heating. Then when the ITB forms, high frequency turbulence is reduced locally within the steep pressure gradient region of the ITB, consistent with the effects of enhanced ExB poloidal shear. The turbulence suppression is correlated with reduced plasma transport and improved fusion performance.