We present the first demonstration of THz driven bunch compression and timing stabilization of a relativistic electron beam. Quasi-single-cycle strong field THz radiation is used in a shorted parallel-plate structure to compress a few-fC beam with 2.5 MeV kinetic energy by a factor of 2.7, producing a 39 fs rms bunch length and a reduction in timing jitter by more than a factor of 2 to 31 fs rms. This THz driven technique offers a significant improvement to beam performance for applications like ultrafast electron diffraction, providing a critical step towards unprecedented timing resolution in ultrafast sciences, and other accelerator applications using femtosecond-scale electron beams.