  A Nijenhuis operator on a manifold $M$ is a $(1,1)$ tensor $\mathcal N$ whose
Nijenhuis-torsion vanishes. A Nijenhuis operator $\mathcal N$ on $M$ determines
a Lie algebroid structure $(TM)_{\mathcal N}$ on the tangent bundle $TM$. In
this sense a Nijenhuis operator can be seen as an infinitesimal object. In this
paper, we identify its "global counterpart". Namely, we show that when the Lie
algebroid $(TM)_{\mathcal N}$ is integrable, then it integrates to a Lie
groupoid equipped with appropriate additional structure responsible for
$\mathcal N$, and viceversa, the Lie algebroid of a Lie groupoid equipped with
such additional structure is of the type $(TM)_{\mathcal N}$ for some Nijenhuis
operator $\mathcal N$. We illustrate our integration result in various
examples.
