  Gl 758 B is a late-T dwarf orbiting a metal-rich Sun-like star at a projected
separation of $\rho$ $\approx$ 1.6" (25 AU). We present four epochs of
astrometry of this system with NIRC2 at Keck Observatory spanning 2010 to 2017
together with 630 radial velocities (RVs) of the host star acquired over the
past two decades from McDonald Observatory, Keck Observatory, and the Automated
Planet Finder at Lick Observatory. The RVs reveal that Gl 758 is accelerating
with an evolving rate that varies between 2-5 m s$^{-1}$ yr$^{-1}$, consistent
with the expected influence of the imaged companion Gl 758 B. A joint fit of
the RVs and astrometry yields a dynamical mass of 42$^{+19}_{-7}$
M$_\mathrm{Jup}$ for the companion with a robust lower limit of 30.5
M$_\mathrm{Jup}$ at the 4-$\sigma$ level. Gl 758 B is on an eccentric orbit
($e$ = 0.26-0.67 at 95% confidence) with a semimajor axis of $a$ =
$21.1_{-1.3}^{+2.7}$ AU and an orbital period of $P$ = $96_{-9}^{+21}$ yr,
which takes it within $\approx$9 AU from its host star at periastron passage.
Substellar evolutionary models generally underpredict the mass of Gl 758 B for
nominal ages of 1-6 Gyr that have previously been adopted for the host star.
This discrepancy can be reconciled if the system is older---which is consistent
with activity indicators and recent isochrone fitting of the host star---or
alternatively if the models are systematically overluminous by $\approx$0.1-0.2
dex. Gl 758 B is currently the lowest-mass directly imaged companion inducing a
measured acceleration on its host star. In the future, bridging RVs and
high-contrast imaging with the next generation of extremely large telescopes
and space-based facilities will open the door to the first dynamical mass
measurements of imaged exoplanets.
