  Hubble Space Telescope observations of the nearby (3.22 pc), K2 V star
epsilon Eridani have been combined with ground-based astrometric and radial
velocity data to determine the mass of its known companion. We model the
astrometric and radial velocity measurements simultaneously to obtain the
parallax, proper motion, perturbation period, perturbation inclination, and
perturbation size. Because of the long period of the companion, \eps b, we
extend our astrometric coverage to a total of 14.94 years (including the three
year span of the \HST data) by including lower-precision ground-based
astrometry from the Allegheny Multichannel Astrometric Photometer. Radial
velocities now span 1980.8 -- 2006.3. We obtain a perturbation period, P = 6.85
+/- 0.03 yr, semi-major axis, alpha =1.88 +/- 0.20 mas, and inclination i =
30.1 +/- 3.8 degrees. This inclination is consistent with a previously measured
dust disk inclination, suggesting coplanarity. Assuming a primary mass M_* =
0.83 M_{\sun}, we obtain a companion mass M = 1.55 +/- 0.24 M_{Jup}. Given the
relatively young age of epsilon Eri (~800 Myr), this accurate exoplanet mass
and orbit can usefully inform future direct imaging attempts. We predict the
next periastron at 2007.3 with a total separation, rho = 0.3 arcsec at position
angle, p.a. = -27 degrees. Orbit orientation and geometry dictate that epsilon
Eri b will appear brightest in reflected light very nearly at periastron.
Radial velocities spanning over 25 years indicate an acceleration consistent
with a Jupiter-mass object with a period in excess of 50 years, possibly
responsible for one feature of the dust morphology, the inner cavity.
