The magnetic field dependence of the Eck step voltage in long Josephson tunnel junctions (LJTJs) can be exploited for ultralownoise magnetic sensing. The magnetic flux to be measured is captured by a non-interrupted superconducting pickup loop in which a narrow constriction, forming the LJTJ wiring layer, produces a local high density circulating currents which, in turn, induces a magnetic field large enough to set a biased LJTJ at a finite voltage proportional to the field strength (flux-flow state). On this basis, an innovative and ultralow-noise superconducting device has been realized having a highly linear voltage responsivity and an intrinsic voltage spectral density down to few pV/√Hz. Being that the intrinsic voltage fluctuations of these all-Niobium sensors are very low (at T = 4.2 K), a double transformer superconducting quantum interference device (SQUID) amplifier has been used to determine the amplitude of its voltage spectral density obtaining a value as low as 10 pV/√Hz. In addition, the 1/f noise does not affect the sensor performance down to a few hertz. The corresponding magnetic field noise, equal to 10 fT/√Hz, together with highly linear and broadband voltage responsivity over a wide magnetic flux range, features performances that are comparable with those of a SQUID magnetometers having a comparable flux capture area.