Luminescent solar concentrators (LSCs) are spectral conversion devices offering interesting opportunities for the integration of photovoltaics into the built environment and portable systems. The Förster-resonance energy transfer (FRET) process can boost the optical response of LSCs by reducing energy losses typically associated to non-radiative processes occurring within the device under operation. In this work, a new class of FRET-based thin-film LSC devices is presented, in which the synthetic versatility of linear polyurethanes (PU) is exploited to control the photophysical properties and the device performance of the resulting LSCs. A series of luminescent linear PUs are synthesized in the presence of two novel bis-hydroxyl-functionalized luminophores of suitable optical properties, used as chain extenders during the step-growth polyaddition reaction for the formation of the linear macromolecular network. By synthetically tuning their composition, the obtained luminescent PUs can achieve a high energy transfer efficiency (≈90%) between the covalently linked luminophores. The corresponding LSC devices exhibit excellent photonic response, with external and internal photon efficiencies as high as ≈4% and ≈37%, respectively. Furthermore, their optimized power conversion efficiency combined with their enhanced average visible-light transmittance highlight their suitability for potential use as transparent solar energy devices.