Inelastic neutron scattering is employed to investigate the impact of electronic nematic order on the magnetic spectra of LaFeAsO and Ba(Fe0.953Co0.047)2As2. These materials are ideal to study the paramagnetic-nematic state, since the nematic order, signaled by the tetragonal-to-orthorhombic transition at TS, sets in well above the stripe antiferromagnetic ordering at TN. We find that the temperature-dependent dynamic susceptibility displays an anomaly at TS followed by a sharp enhancement in the spin-spin correlation length, revealing a strong feedback effect of nematic order on the low-energy magnetic spectrum. Our findings can be consistently described by a model that attributes the structural or nematic transition to magnetic fluctuations, and unveils the key role played by nematic order in promoting the long-range stripe antiferromagnetic order in iron pnictides.