Minimization or tailoring of magnetic anisotropies in the order of magneto-crystal, magneto-elastic and external field-induced anisotropies are effective way of improving soft-magnetism in nanocrystalline alloys. The recently developed Fe-rich nanocrystalline alloys have been found to exhibit positive magnetostriction behaviour and magnetic coercivity twice that of FINEMET alloys, after optimal annealing. This makes uniaxial tensile-stress annealing a promising method to improve the soft-magnetism of these alloys. In that direction, the present study investigates the influence of tensile stress annealing on structure, soft-magnetic, magnetostriction and core-loss properties of Fe-rich Fe83Si2B9P4Nb1Cu1 nanocrystalline ribbons. The samples were uniformly annealed at 480 °C for 4 min with varying uniaxial tensile stress ranging from 0 to 180 MPa. The XRD results showed that all annealed ribbons had a uniform nanocrystalline microstructure consisting of a BCC α-Fe(Si) phase with an average grain size of less than 20 nm, irrespective of the applied stress. However, the magnetic properties were highly sensitive to the magnitude of the tensile stress during nanocrystallization annealing. The optimal tensile stress ranging from 90-140 MPa resulted in the best combination of soft-magnetic properties (11–12 A/m) and high squareness ratio (0.8-0.9). These ribbons also depicted longitudinal anisotropy (Ku ≤ 0). On the other hand, tensile stress above 165 MPa resulted in the deterioration of magnetic properties (> 24 A/m) and transverse anisotropy behaviour (Ku > 0). The transformation of tensile stress-induced anisotropy from longitudinal to transverse was characterized by the reduction of the magnetostriction constant and change in the magnetization process. The core-loss plots (50-1000 Hz) showed a reduction for optimal stress-annealed (90-140 MPa) ribbons and a drastic increase for 165-180 MPa ribbons. The study highlights the beneficial role of controlled tensile stress annealing in improving the soft-magnetism of Fe-rich nanocrystalline alloys with positive magnetostriction.