We propose and demonstrate a method to reduce the pulse width and timing jitter of a relativistic electron beam through THz driven beam compression. In this method the longitudinal phase space of a relativistic electron beam is manipulated by a linearly polarized THz pulse copropagating in a dielectric tube such that the bunch tail has a higher velocity than the bunch head, which allows simultaneous reduction of both pulse width and timing jitter after passing through a drift. In this experiment, the beam is compressed by more than a factor of 4 from 130 fs to 28 fs with the arrival time jitter also reduced from 97 fs to 36 fs, opening up new opportunities in using pulsed electron beams for studies of ultrafast dynamics. This technique provides an effective way to manipulate beam longitudinal phase space with a THz pulse and may have a strong impact in accelerator and ultrafast science facilities that require femtosecond electron beams with tight synchronization to external lasers.