In iron-based superconductors the interactions driving the nematic order (that breaks four-fold rotational symmetry in the iron plane) may also mediate the Cooper pairing(1). The experimental determination of these interactions, which are believed to depend on the orbital or the spin degrees of freedom(1-4), is challenging because nematic order occurs at, or slightly above, the ordering temperature of a stripe magnetic phase(1,5). Here, we study FeSe (ref.6)-which exhibits a nematic (orthorhombic) phase transition at Ts = 90 K without antiferromagnetic ordering-by neutron scattering, finding substantial stripe spin fluctuations coupled with the nematicity that are enhanced abruptly on cooling through Ts. A sharp spin resonance develops in the superconducting state, whose energy (similar to 4 meV) is consistent with an electron-boson coupling mode revealed by scanning tunnelling spectroscopy(7). The magnetic spectralweight in FeSe is found to be comparable to that of the iron arsenides(8,9). Our results support recent theoretical proposals that both nematicity and superconductivity are driven by spin fluctuations(1,10-13).