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.
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