  LP~349$-$25 is a well studied close stellar binary system comprised of two
late M dwarf stars, both stars close to the limit between star and brown dwarf.
This system was previously identified as a source of GHz radio emission. We
observed LP~349$-$25AB in 11 epochs in 2020$-$2022, detecting both components
in this nearby binary system using the Very Long Baseline Array (VLBA). We fit
simultaneously the VLBA absolute astrometric positions together with existing
relative astrometric observations derived from optical/infrared observations
with a set of algorithms that use non-linear least-square, Genetic Algorithm
and Markov Chain Montecarlo methods to determine the orbital parameters of the
two components. We find the masses of the primary and secondary components to
be 0.08188 $\pm$ 0.00061 $M\odot$, and 0.06411 $\pm$ 0.00049 $M_\odot$,
respectively, representing one of the most precise mass estimates of any UCDs
to date. The primary is an UCD of 85.71$\pm$0.64 M$_{Jup}$, while the secondary
has a mass consistent with being a Brown Dwarf of 67.11 $\pm$ 0.51 $M_{Jup}$.
This is one of the very few direct detections of a Brown Dwarf with VLBA
observations. We also find a distance to the binary system of 14.122 $\pm$
0.057 pc. Using Stellar Evolutionary Models, we find the model-derived stellar
parameters of both stars. In particular, we obtain a model-derived age of 262
Myr for the system, which indicates that LP~349$-$25AB is composed of two
pre-main-sequence stars. In addition, we find that the secondary star is
significantly less evolved that the primary star.
