We report the successful identification of the type of the supernova (SN) responsible for the supernova remnant SNR 0509–675 in the Large Magellanic Cloud (LMC) using Gemini spectra of surrounding light echoes. The ability to classify outbursts associated with centuries-old remnants provides a new window into several aspects of SN research and is likely to be successful in providing new constraints on additional LMC SNe, as well as their historical counterparts in the Milky Way (MW). The combined spectrum of echo light from SNR 0509–675 shows broad emission and absorption lines consistent with a SN spectrum. We create a spectral library consisting of 28 SNe Ia and 6 SNe Ib/c that are time-integrated, dust-scattered by LMC dust, and reddened by the LMC and MW. We fit these SN templates to the observed light echo spectrum using\chi^{2} minimization, as well as correlation techniques, and we find that overluminous 1991T-like SNe Ia with\Delta m_ {15}< 0.9 match the observed spectrum best.