We introduce the importance of edge modes in the evaluation of entanglement entropy of subregions in U(1) gauge theory. We evaluate the contribution of these modes towards the universal logarithmic coefficient of entanglement across a spherical spatial region in U(1) gauge theory in even d dimensions. We show that this agrees with the logarithmic divergent part of the edge Harish-Chandra character of the theory on the d-sphere. We then consider the theory of linearized gravitons in 4 space-time dimensions. Quantizing the theory in tensor spherical harmonics we evaluate the contribution of the edge modes of the graviton towards the entanglement of a spatial region. We observe that this coefficient coincides with that extracted from the edge Harish-Chandra character of the massless spin-2 field on the S^4.