Observations of extremely low frequency (ELF) radio atmospherics (sferics), the transient electromagnetic fields radiated by lightning discharges, are used to determine the current moment waveforms of vertical lightning discharges. In order to extract this information the propagation of radio atmospherics from source to receiver must be modeled accurately, especially in view of the important role played by the D and E regions of the ionosphere at these long (> 200 km) wavelengths. We model broadband ELF sferic waveforms by adapting a single-frequency ELF propagation code to calculate an ELF propagation impulse response under the assumption of horizontal ionospheric homogeneity, with which we extract the source lightning current waveform from an observed ELF sferic waveform using a deconvolution method based on linear regularization. Tests on modeled sferics indicate that the method is accurate and relatively insensitive to noise, and we demonstrate the application of the technique with a sprite-associated sferic. Since ELF sferics can often be observed many thousands of kilometers from the source discharge, the technique developed here represents a powerful new method of remotely sensing lightning current waveforms.