We exploit the first Gaia data release to study the properties of the Galactic stellar halo as traced by RR Lyrae. We demonstrate that it is possible to select a pure sample of RR Lyrae using only photometric information available in the Gaia+2MASS catalogue. The final sample contains about 21 600 RR Lyrae covering an unprecedented fraction ( ∼ 60 per cent) of the volume of the Galactic inner halo (R < 28 kpc). We study the morphology of the stellar halo by analysing the RR Lyrae distribution with parametric and non-parametric techniques. Taking advantage of the uniform all-sky coverage, we test halo models more sophisticated than usually considered in the literature, such as those with varying flattening, tilts and/or offset of the halo with respect to the Galactic disc. A consistent picture emerges: the inner halo is well reproduced by a smooth distribution of stars settled on triaxial density ellipsoids. The shortest axis is perpendicular to the Milky Way's disc, while the longest axis forms an angle of ∼70° with the axis connecting the Sun and the Galactic Centre. The elongation along the major axis is mild (p = 1.27), and the vertical flattening is shown to evolve from a squashed state with q ≈ 0.57 in the centre to a more spherical q ≈ 0.75 at the outer edge of our data set. Within the radial range probed, the density profile of the stellar halo is well approximated by a single power law with exponent α = −2.96. We do not find evidence of tilt or offset of the halo with respect to the Galaxy's disc.