  We report individual dynamical masses of $66.92 \pm 0.36 \; M_{Jup}$ and
$53.25 \pm 0.29 \; M_{Jup}$ for the binary brown dwarfs $\varepsilon$ Indi Ba
and Bb, measured from long term ($\approx 10$ yr) relative orbit monitoring and
absolute astrometry monitoring data on the VLT. Relative astrometry with NACO
fully constrains the Keplerian orbit of the binary pair, while absolute
astrometry with FORS2 measures the system's parallax and mass ratio. We find a
parallax consistent with the Hipparcos and Gaia values for $\varepsilon$ Indi
A, and a mass ratio for $\varepsilon$ Indi Ba to Bb precise to better than
$0.2\%$. $\varepsilon$ Indi Ba and Bb have spectral types T1-1.5 and T6,
respectively. With an age of $3.5^{+0.8}_{-1.0}$ Gyr from $\varepsilon$ Indi
A's activity, these brown dwarfs provide some of the most precise benchmarks
for substellar cooling models. Assuming coevality, the very different
luminosities of the two brown dwarfs and our moderate mass ratio imply a steep
mass-luminosity relationship $L \propto M^{5.37 \pm 0.08}$ that can be
explained by a slowed cooling rate in the L/T transition, as previously
observed for other L/T binaries. Finally, we present a periodogram analysis of
the near-infrared photometric data, but find no definitive evidence of periodic
signals with a coherent phase.
