  In this article we explicitly determine the structure of the Weierstrass
semigroups $H(P)$ for any point $P$ of the Giulietti-Korchm\'aros curve
$\mathcal{X}$. We show that as the point varies, exactly three possibilities
arise: One for the $\mathbb{F}_{q^2}$-rational points (already known in the
literature), one for the $\mathbb{F}_{q^6} \setminus \mathbb{F}_{q^2}$-rational
points, and one for all remaining points. As a result, we prove a conjecture
concerning the structure of $H(P)$ in case $P$ is an $\mathbb{F}_{q^6}
\setminus \mathbb{F}_{q^2}$-rational point. As a corollary we also obtain that
the set of Weierstrass points of $\mathcal{X}$ is exactly its set of
$\mathbb{F}_{q^6}$-rational points.
