WISE J104915.57$-$531906.1 is a L/T brown dwarf binary located 2pc from the Sun. The pair contains the closest known brown dwarfs and is the third closest known system, stellar or sub-stellar. We report comprehensive follow-up observations of this newly uncovered system. We have determined the spectral types of both components (L8+/-1, for the primary, agreeing with the discovery paper; T1.5+/-2 for the secondary, which was lacking spectroscopic type determination in the discovery paper) and, for the first time, their radial velocities (V_rad~23.1, 19.5 km/s) using optical spectra obtained at the Southern African Large Telescope (SALT) and other facilities located at the South African Astronomical Observatory (SAAO). The relative radial velocity of the two components is smaller than the range of orbital velocities for theoretically predicted masses, implying that they form a gravitationally bound system. We report resolved near-infrared JHK_S photometry from the IRSF telescope at the SAAO which yields colors consistent with the spectroscopically derived spectral types. The available kinematic and photometric information excludes the possibility that the object belongs to any of the known nearby young moving groups or associations. Simultaneous optical polarimetry observations taken at the SAAO 1.9-m give a non-detection with an upper limit of 0.07%. For the given spectral types and absolute magnitudes, 1Gyr theoretical models predict masses of 0.04--0.05 M_odot for the primary, and 0.03--0.05 M_odot for the secondary. ; Comment: 5 pages, 3 figures, Accepted to Astrophysical Journal