  Cygnus X-1 is a binary star system that is comprised of a black hole and a
massive giant companion star in a tight orbit. Building on our accurate
distance measurement reported in the preceding paper, we first determine the
radius of the companion star, thereby constraining the scale of the binary
system. To obtain a full dynamical model of the binary, we use an extensive
collection of optical photometric and spectroscopic data taken from the
literature. By using all of the available observational constraints, we show
that the orbit is slightly eccentric (both the radial velocity and photometric
data independently confirm this result) and that the companion star rotates
roughly 1.4 times its pseudosynchronous value. We find a black hole mass of M
=14.8\pm1.0 M_{\sun}, a companion mass of M_{opt}=19.2\pm1.9 M_{\sun}, and the
angle of inclination of the orbital plane to our line of sight of i=27.1\pm0.8
deg.
