  For a fixed finite set of finite tournaments ${\mathcal F}$, the ${\mathcal
F}$-free orientation problem asks whether a given finite undirected graph $G$
has an $\mathcal F$-free orientation, i.e., whether the edges of $G$ can be
oriented so that the resulting digraph does not embed any of the tournaments
from ${\mathcal F}$. We prove that for every ${\mathcal F}$, this problem is in
P or NP-complete. Our proof reduces the classification task to a complete
complexity classification of the orientation completion problem for ${\mathcal
F}$, which is the variant of the problem above where the input is a directed
graph instead of an undirected graph, introduced by Bang-Jensen, Huang, and Zhu
(2017). Our proof uses results from the theory of constraint satisfaction, and
a result of Agarwal and Kompatscher (2018) about infinite permutation groups
and transformation monoids.
