System for displacing a blowout prevention safety valve, which has an overhead crane mounted on a suspended rail and provided with a winch for lifting and transporting the safety valve from a parking zone to a drilling area, where a crane is placed on which the safety valve is hung. A coupling device is mounted on the overhead crane, such that the overhead crane can be moved between the parking zone and the drilling area, having both the winch and the coupling device connected to the safety valve. In the drilling area, the coupling device are disengaged from the safety valve, while the crane and the winch are maintained connected to the safety valve in order to lower it to an operating position.