A new, transient ultraluminous X-ray source (ULX) was recently discovered by Chandra in M31 with a luminosity at ∼5 × 10 39 erg s −1 . Here we analyse a series of five subsequent XMM-Newton observations. These show a steady decline in X-ray luminosity over 1.5 months, from 1.8 × 10 39 to 0.6 × 10 39 erg s −1 , giving an observed e-fold time-scale of ∼40 d. This is similar to the decay time-scales seen in multiple soft X-ray transients in our own Galaxy, supporting 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 spectral behaviour of the XMM-Newton 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 in full frame mode. The spectra can be roughly described by our best current disc model, BHSPEC, assuming a 10 M black hole with best-fitting spin ∼0.4, declining from L/L Edd = 0.75 to 0.25. However, the data are better described by a twocomponent model, where the disc emission is significantly affected by advection, and with an additional low-temperature Comptonization component at high energies which becomes more important at high luminosities. This could simply indicate the limitations of our current disc models, though changes in the energy-dependent variability also weakly supports a twocomponent interpretation of the data.Irrespective of the detailed interpretation of the spectral properties, these data support the presence of accretion on to 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.