A connecting arrangement for connecting a syringe to an electromechanical pump for drug infusion is provided. The syringe comprises a hollow cylindrical syringe body having a first, tapered open end for discharging the drug and a second open end. The syringe body is surrounded by connecting means arranged to firmly connect the syringe to the pump in a removable manner, an axially sliding plunger being housed in the syringe body for causing suction and injection of the drug through the first end. The pump comprises a pump body housing electromechanical members comprising a sliding rod partially projecting out of the pump body to cause sliding of the plunger within the syringe body of the syringe connected to the pump. The pump body being provided with connecting means arranged to receive in an engaging configuration the syringe body. The connecting means provided on the pump body comprise a cylindrical collar axially extending around the sliding rod and being internally provided with engaging elements, the collar defining a sealing end. The connecting means surrounding the syringe body comprise engaging elements arranged to cooperate with the engaging elements provided in the collar for firmly connecting the syringe to the pump in a removable manner. An annular flange extends radially around the syringe body. The flange cooperates with the sealing end defined in the collar to establish a tight sealing between the syringe body and the collar, whereby, when the syringe is attached to the pump, any moisture that may be present in the surrounding environment outside the pump and the syringe attached thereto does not penetrate into the pump body.