We present here the results of astrometric, photometric and spectroscopic observations leading to the determination of the orbit and dynamical masses of the binary L dwarf 2MASSW J0746425+2000321. High angular resolution observations spread over almost 4 years and obtained with the Hubble Space Telescope (HST), the ESO Very Large Telescope (VLT), and a the W. M. Keck Observatory (Keck) allow us to cover ˜36% of the period, corresponding to 60% of the orbit, and, for the first time, to derive a precise estimate of the total and individual masses of such a late-type object. We find an orbital period of 3850.9+904-767 days. The corresponding total mass is 0.146+0.016-0.006 M⊙ with uncertainties depending on the distance. Spatially resolved low resolution optical (550-1025 nm) spectra have been obtained with HST/STIS, allowing us to measure the spectral types of the two components (L0± 0.5 for the primary and L1.5 ±0.5 for the secondary). We also present precise photometry of the individual components measured on the high angular resolution images obtained with HST/ACS and WFPC2 (visible), VLT/NACO (J, H and KS bands) and Keck I (KS band). These spectral and photometric measurements enable us to estimate their effective temperatures and mass ratio, and to place the object accurately in a H-R diagram. The binary system is most likely formed by a primary with a mass of 0.085±0.010 M⊙ and a secondary with a mass of 0.066±0.006 M⊙, thus clearly substellar, for an age of approximately 300±150 Myr. Hα variability indicates chromospheric and/or magnetic activity.Based on observations obtained with the the NASA/ESA Hubble Space Telescope, the ESO Very Large Telescope (program 70.D-0773), and the W. M. Keck Observatory.