We describe the design and deployment of GREENBURST, a commensal Fast Radio Burst (FRB) search system at the Green Bank Telescope. GREENBURST uses the dedicated L-band receiver tap to search over the 960–1 920 MHz frequency range for pulses with dispersion measures out to $10^4\ \rm{pc\,cm}^{-3}$ . Due to its unique design, GREENBURST is capable of conducting searches for FRBs when the L-band receiver is not being used for scheduled observing. This makes it a sensitive single pixel detector capable of reaching deeper in the radio sky. While single pulses from Galactic pulsars and rotating radio transients will be detectable in our observations, and will form part of the database we archive, the primary goal is to detect and study FRBs. Based on recent determinations of the all-sky rate, we predict that the system will detect approximately one FRB for every 2–3 months of continuous operation. The high sensitivity of GREENBURST means that it will also be able to probe the slope of the FRB fluence distribution, which is currently uncertain in this observing band.