The iron chalcogenide Fe(1+y)(Te(1-x)Se(x)) is structurally the simplest of the Fe-based superconductors. Although the Fermi surface is similar to iron pnictides, the parent compound Fe(1+y)Te exhibits antiferromagnetic order with an in-plane magnetic wave vector (pi,0) (ref. 6). This contrasts the pnictide parent compounds where the magnetic order has an in-plane magnetic wave vector (pi,pi) that connects hole and electron parts of the Fermi surface. Despite these differences, both the pnictide and chalcogenide Fe superconductors exhibit a superconducting spin resonance around (pi,pi) (refs 9, 10, 11). A central question in this burgeoning field is therefore how (pi,pi) superconductivity can emerge from a (pi,0) magnetic instability. Here, we report that the magnetic soft mode evolving from the (pi,0)-type magnetic long-range order is associated with weak charge carrier localization. Bulk superconductivity occurs as magnetic correlations at (pi,0) are suppressed and the mode at (pi, pi) becomes dominant for x>0.29. Our results suggest a common magnetic origin for superconductivity in iron chalcogenide and pnictide superconductors.