A tensioner for a belt transmission of a motor vehicle engine has a fixed part configured to be constrained to the engine and provided with a pin defining a rotation axis (A), an arm having a hub portion hinged on the pin and rotatable about the axis (A) and an opposite portion rotatably supporting a pulley configured to cooperate with a transmission belt, a main spring interposed between the fixed part and the arm to exert a thrust on the arm such as to rotate the arm towards the belt, a roller bearing supporting the arm on the pin, and a pair of damping devices exerting on the arm opposite actions so as to minimize the load on the bearing.