We report the discovery of a T8.5 dwarf, which is a companion to the M4 dwarf Wolf 940. At a distance of 12.50+0.75-0.67 pc, the angular separation of 32 arcsec corresponds to a projected separation of 400 au. The M4 primary displays no Hα emission, and we apply the age-activity relations of West et al. to place a lower limit on the age of the system of 3.5 Gyr. Weak Hα absorption suggests some residual activity, and we estimate an upper age limit of 6 Gyr. We apply the relations of Bonfils et al. for V - Ks and to determine the metallicity, [Fe/H] = -0.06 +/- 0.20 for Wolf 940A, and by extension the T8.5 secondary, Wolf 940B. We have obtained JHK NIRI spectroscopy and JHKL' photometry of Wolf 940B, and use these data, in combination with theoretical extensions, to determine its bolometric flux, Fbol = 1.75 +/- 0.18 × 10-16Wm-2, and thus its luminosity log(L*/Lsolar) = -6.07 +/- 0.04. Using the age constraints for the system and evolutionary structural models of Baraffe et al., we determine Teff = 570 +/- 25K and logg = 4.75 - 5.00 for Wolf 940B, based on its bolometric luminosity. This represents the first determination of these properties for a T8+ dwarf that does not rely on the fitting of T dwarf spectral models. This object represents the first system containing a T8+ dwarf for which fiducial constraints on its properties are available, and we compare its spectra with those of the latest very cool BT-Settl models. This clearly demonstrates that the use of the (WJ, K/J) spectral ratios (used previously to constrain Teff and logg) would have overestimated Teff by ~100K.