Fuel-free magnetically driven propulsion of flexible Au/Ag/Ni nanowires, with a gold 'head' and nickel 'tail', linked by a partially dissolved and weakened silver bridge, is described. The flexible bridge facilitates the cyclic mechanical deformations under an external rotating magnetic field. Under such a field the nickel segment starts to rotate, facilitating the rotation of the gold segment at a different amplitude, hence breaking the system symmetry and inducing the movement. Forward ('pushing') and backward ('pulling') magnetically powered locomotion and a precise On/Off motion control are achieved by tailoring the length of the nickel and gold segments and modulating the magnetic field, respectively. Efficient locomotion in urine samples and in high-salt media is illustrated. The new magnetic nanowire swimmers can be prepared in large scale using a simple template electrodeposition protocol and offer considerable promise for diverse practical applications.