We compute the nonlinear memory contributions to the gravitational-wave amplitudes for compact binaries in eccentric orbits at the third post-Newtonian (3PN) order in general relativity. These contributions are hereditary in nature as they are sourced by gravitational waves emitted during the binary's entire dynamical past. Combining these with already available instantaneous and tail contributions, we get the complete 3PN accurate gravitational waveform. © 2019 American Physical Society.