The iron chalcogenide Fe1+y(Te1-xSex) is structurally the simplest of the Fe-based superconductors(1-3). Although the Fermi surface is similar to iron pnictides(4,5), the parent compound Fe1+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(7,8). Despite these differences, both the pnictide and chalcogenide Fe superconductors exhibit a superconducting spin resonance around (pi,pi) (refs 9-11). A central question in this burgeoning field is therefore how(pi,pi) superconductivity can emerge from a (pi,0) magnetic instability(12). 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.