The morphological properties of the outflowing circumstellar envelopes surrounding mass-losing stars in eccentric binary systems are presented based upon the results from a set of three-dimensional hydrodynamical model simulations. Making use of four template models of the envelope viewed for a range of inclination angles of the systems, we implement interpretative tools for observations at high spectral/angular resolutions (as illustrated via velocity-channel maps as well as position？velocity, radius？velocity, and angle？radius diagrams). Within this framework, the image and kinematical structures can be used to place constraints on the orbital parameters of the system. Specifically, three unique characteristic patterns in the envelopes are found that distinguish these systems from those in binary systems in circular orbits. Bifurcation of the spiral pattern, asymmetry in the interarm density depression, and a concurrent spiral/ring appearance all point to a binary system with an eccentric orbit. The methodology presented in this paper is illustrated in an analysis of recent radio observations of several asymptotic giant branch stars.