An assembly for inclusion between a drill bit and a drill string, the assembly having an overrunning clutch mechanism that disengages the drill bit from the drill string during the “slip” portion of a stick-slip cycle to allow the drill bit to freely rotate faster than the drill string. The assembly further includes a rotational vibration dampener operatively connected between the overrunning clutch and the drill bit. The vibration dampener may include a fluid chamber with viscous fluid or restrictions to fluid flow to effect dampening. During normal operation, the one-way overrunning clutch remains engaged to transfer torque between the drill string and bit, while the torsional damper is in its maximum displaced position to transfer the load. During slip, the drill bit is disengaged until its speed is lower than the drill string speed. Torsional vibration dampener dampens sudden impulse force of the overrunning clutch re-engaging.