  Hypervelocity stars (HVSs) are amongst the fastest objects in our Milky Way.
These stars are predicted to come from the Galactic center (GC) and travel
along unbound orbits across the Galaxy. In the coming years, the ESA satellite
Gaia will provide the most complete and accurate catalogue of the Milky Way,
with full astrometric parameters for more than $1$ billion stars. In this
paper, we present the expected sample size and properties (mass, magnitude,
spatial, velocity distributions) of HVSs in the Gaia stellar catalogue. We
build three Gaia mock catalogues of HVSs anchored to current observations,
exploring different ejection mechanisms and GC stellar population properties.
In all cases, we predict hundreds to thousands of HVSs with precise proper
motion measurements within a few tens of kpc from us. For stars with a relative
error in total proper motion below $10 \%$, the mass range extends to ~$10
M_{\odot}$ but peaks at ~$1$ $M_\odot$. The majority of Gaia HVSs will
therefore probe a different mass and distance range compared to the current
non-Gaia sample. In addition, a subset of a few hundreds to a few thousands of
HVSs with $M$ ~ $3$ $M_\odot$ will be bright enough to have a precise
measurement of the three-dimensional velocity from Gaia alone. Finally, we show
that Gaia will provide more precise proper motion measurements for the current
sample of HVS candidates. This will help identifying their birthplace narrowing
down their ejection location, and confirming or rejecting their nature as HVSs.
Overall, our forecasts are extremely encouraging in terms of quantity and
quality of HVS data that can be exploited to constrain both the Milky Way
potential and the GC properties.
