We have developed a full waveform inversion (FWI) algorithm for the seismic-while-drilling (SWD) dataset. Full waveform inversion is a local optimization method. To avoid the local minima, seismic data should have rich low-frequency content. However, in the real-world, seismic data lacks low-frequency content, and FWI struggles to provide accurate subsurface properties. To remedy this shortcoming, we use SWD data to compensate for the lack of low frequencies in the surface seismic dataset. In SWD data, the drillbit acts as a seismic source. The drillbit generates significant elastic energy, which has different raypaths compared to the surface seismic. We show that if we understand the non-impulsive and correlative behavior of the drillbit source signature, the full waveform inversion of SWD data is possible. To estimate the drillbit source signature, we have developed a computational framework based on wave equation drill string dynamics modeling along with top-drive force and velocity measurements. Then, we feed the estimated dillbit source signature to the FWI algorithm to invert the SWD dataset. Our results show that the successive inversion of surface seismic and SWD datasets can compensate for the lack of low frequencies in the surface seismic data and reduce the uncertainties of the subsurface properties.