The structure of the edge plasma in a magnetic confinement system has a strong impact on the overall plasma performance. We uncover for the first time a magnetic-field-direction dependent density shelf, i.e., local flattening of the density radial profile near the magnetic separatrix, in high confinement plasmas with low edge collisionality in the DIII-D tokamak. The density shelf is correlated with a doubly peaked density profile near the divertor target plate, which tends to occur for operation with the ion B x del B drift direction away from the X-point, as currently employed for DIII-D advanced tokamak scenarios. This double-peaked divertor plasma profile is connected via the E x B drifts, arising from a strong radial electric field induced by the radial electron temperature gradient near the divertor target. The drifts lead to the reversal of the poloidal flow above the divertor target, resulting in the formation of the density shelf. The edge density shelf can be further enhanced at higher heating power, preventing large, periodic bursts of the plasma, i.e., edge-localized modes, in the edge region, consistent with ideal magnetohydrodynamics calculations.