  We study Hanbury-Brown and Twiss current cross-correlations in a
three-terminal junction where a central topological superconductor (TS)
nanowire, bearing Majorana bound states at its ends, is connected to two normal
leads. Relying on a non-perturbative Green function formalism, our calculations
allow us to provide analytical expressions for the currents and their
correlations at subgap voltages, while also giving exact numerical results
valid for arbitrary external bias. We show that when the normal leads are
biased at voltages $V_1$ and $V_2$ smaller than the gap, the sign of the
current cross-correlations is given by $-\mbox{sgn}(V_1 \, V_2)$. In
particular, this leads to positive cross-correlations for opposite voltages, a
behavior in stark contrast with the one of a standard superconductor, which
provides a direct evidence of the presence of the Majorana zero-mode at the
edge of the TS. We further extend our results, varying the length of the TS
(leading to an overlap of the Majorana bound states) as well as its chemical
potential (driving it away from half-filling), generalizing the boundary TS
Green function to those cases. In the case of opposite bias voltages,
$\mbox{sgn}(V_1 \, V_2)=-1$, driving the TS wire through the topological
transition leads to a sign change of the current cross-correlations, providing
yet another signature of the physics of the Majorana bound state.
