Femtosecond relativistic electron bunches and micro-bunch trains synchronised with femtosecond precision to external laser sources are widely sought for next-generation accelerator and photonic technologies, from extreme UV and X-ray light sources for materials science, to ultrafast electron diffraction and future high-energy physics colliders. While few-femtosecond bunches have been demonstrated, achieving the control, stability and femtosecond-level laser synchronisation remains critically out of reach. Here we demonstrate a concept for laser-driven compression of high-energy (35.5 MeV) electron bunches with temporal synchronisation to a high-power (few-TW) laser system. Laser-generated multi-cycle terahertz (THz) pulses drive periodic electron energy modulation, enabling subsequent magnetic compression capable of generating tuneable picosecond-spaced bunch trains with 30 pC total charge and 50 A peak currents, or to compress a single bunch by a factor of 27 down to 15 fs duration. The THz-driven compression simultaneously drives temporal-locking of the bunch to the THz drive laser, providing a route to femtosecond-level synchronisation, overcoming the timing jitter inherent to radio-frequency accelerators and high-power laser systems. This THz technique offers compact and flexible bunch control with unprecedented temporal synchronisation, opening a pathway to unlock new capabilities for free electron lasers, ultrafast electron diffraction and novel plasma accelerators.