The recently discovered star SCR 1845-6357 is the first late M/T dwarf binary discovered. SCR 1845 is a particular object due to its tight orbit (currently around 4 AU) and its proximity to the Sun (3.85 pc). We present spatially resolved VLT/NACO images and low resolution spectra of SCR 1845 in the J, H and K near-infrared bands. Since the T dwarf companion, SCR 1845B, is so close to the primary SCR 1845A, orbital motion is evident even within a year. Following the orbital motion, the binarys mass can be measured accurately within a decade, making SCR 1845B a key T-dwarf mass-luminosity calibrator. The NIR spectra allow for accurate determination of spectral type and also for rough estimates of the objects physical parameters. The spectral type of SCR 1845B is determined by direct comparison of the flux calibrated JHK spectra with T dwarf standard template spectra and also by NIR spectral indices obtained from synthetic photometry. Constrained values for surface gravity, effective temperature and metallicity are derived by comparison with model spectra. Our data prove that SCR 1845B is a brown dwarf of spectral type T6 that is co-moving with and therefore gravitationally bound to the M8.5 primary. Fitting the NIR spectrum of SCR 1845B to model spectra yields an effective temperature of about 950K and a surface gravity log(g)=5.1 (cgs) assuming solar metallicity. Mass and age of SCR 1845B are in the range 40 to 50 Jupiter masses and 1.8 to 3.1 Gyr.