A new, transient ultraluminous X-ray source (ULX) was recently discovered by Chandra in M31 with a luminosity at ~ 5 x 10^39 erg/s. Here we analyse a series of five subsequent XMM-Newton observations. The steady decline in X-ray luminosity over 1.5 months gives an observed e-fold timescale of ~40 days; similar to the decay timescales seen in soft X-ray transients in our own Galaxy. This supports the interpretation of this ULX as a stellar mass black hole in a low-mass X-ray binary (LMXB), accreting at super Eddington rates. This is further supported by the lack of detection of an O/B star in quiescence and the XMM-Newton spectral data being dominated by a disc-like component rather than the power-law expected from a sub-Eddington intermediate-mass black hole. These data give the best sequence of high Eddington fraction spectra ever assembled due to the combination of low absorption column to M31 and well calibrated bandpass down to 0.3 keV of XMM-Newton. The spectra can be roughly described by our best current disc model, BHSPEC, assuming a 10 M_solar black hole with best fit spin of ~0.4. However, the data are better described by a two component model, where the disc emission is significantly affected by advection, and with an additional low temperature Comptonisation component at high energies. This could simply indicate the limitations of current disc models, though the energy-dependent variability also weakly supports a two component interpretation of the data. Irrespective of the detailed interpretation of the spectral properties, these data support the presence of accretion onto a stellar mass black hole in a LMXB accreting in the Eddington-regime. This allows an unambiguous connection of this object, and, by extension, similar low luminosity ULXs, to `standard' X-ray binaries.