The analytic signal concept can be applied to gravity gradient tensor data in three dimensions. Within the gravity gradient tensor, the horizontal and vertical derivatives of gravity vector components are Hilbert transform pairs. Three analytic signal functions then are introduced along x-, y-, and z-directions. The amplitude of the first vertical derivative of the analytic signals in x- and y-directions enhances the edges of causative bodies. The directional analytic signals are homogenous and satisfy Euler's homogeneity equation. The application of directional analytic signals to Euler deconvolution on generic models demonstrates their ability to locate causative bodies. One of the advantages of this method is that it allows the automatic identification of the structural index from solving three Euler equations derived from the gravity gradient tensor for a collection of data points in a window. The other advantage is a reduction of interference effects from neighboring sources by differentiation of the directional analytic signals in x-, y-, and z-directions. Application of the method is demonstrated on gravity gradient tensor data in the Vredefort impact structure, South Africa.