A Time-Delay Integration (TDI) image processing system has been developed to capture ICON's Far Ultraviolet (FUV) Spectrographic Imager data. The TDI system is designed to provide variable-range motion-compensated imaging of Earth's nightside ionospheric limb and sub-limb scenes viewed from Low Earth Orbit in the 135.6 nm emission of oxygen with an integration time of 12 seconds. As a pre-requisite of the motion compensation the TDI system is also designed to provide corrections for optical distortions generated by the FUV Imager's optical assembly. On the dayside the TDI system is used to process 135.6 nm and 157.0 nm wavelength altitude profiles simultaneously. We present the TDI system's design methodology and implementation as an FPGA module with an emphasis on minimization of on-board data throughput and telemetry. We also present the methods and results of testing the TDI system in simulation and with Engineering Ground Support Equipment (EGSE) to validate its performance.