  We give an explicit presentation for the integral cohomology ring of the
complement of any arrangement of level sets of characters in a complex torus
(alias "toric arrangement"). Our description parallels the one given by Orlik
and Solomon for arrangements of hyperplanes, and builds on De Concini and
Procesi's work on the rational cohomology of unimodular toric arrangements. As
a byproduct we extend Dupont's rational formality result to formality over
$\mathbb Z$.
  The data needed in order to state the presentation is fully encoded in the
poset of connected components of intersections of the arrangement.
