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 \sim 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 _ { \sun } , 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 \pm 0.5 for the primary and L1.5 \pm 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 K _ { S } bands ) and Keck I ( K _ { S } 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 \pm 0.010 M _ { \sun } and a secondary with a mass of 0.066 \pm 0.006 M _ { \sun } , thus clearly substellar , for an age of approximately 300 \pm 150 Myr . H \alpha variability indicates chromospheric and/or magnetic activity .