  A graph of order $n$ is distance magic if it admits a bijective labeling of
its vertices with integers from $1$ to $n$ such that each vertex has the same
sum of the labels of its neighbors. In this paper we classify all distance
magic Cartesian products of two cycles, thereby correcting an error in a widely
cited paper from 2004. Additionally, we show that each distance magic labeling
of a Cartesian product of cycles is determined by a pair or quadruple of
suitable sequences, thus obtaining a complete characterization of all distance
magic labelings of these graphs. We also determine a lower bound on the number
of all distance magic labelings of $C_{m} \square C_{2m}$ with $m \ge 3$ odd.
