Gaia Data Release 3 contains accurate photometric observations of more than 150000 asteroids covering a time interval of 34 months. With a total of about 3000000 measurements, a typical number of observations per asteroid ranges from a few to several tens. We aimed to reconstruct the spin states and shapes of asteroids from this dataset. We computed the viewing and illumination geometry for each individual observation and used the light curve inversion method to find the best-fit asteroid model, which was parameterized by the sidereal rotation period, the spin axis direction, and a low-resolution convex shape. To find the best-fit model, we ran the inversion for tens of thousands of trial periods on interval 2-10000h, with tens of initial pole directions. To find the correct rotation period, we also used a triaxial ellipsoid model for the shape approximation. In most cases the number of data points was insufficient to uniquely determine the rotation period. However, for about 8600 asteroids we were able to determine the spin state uniquely together with a low-resolution convex shape model. This large sample of new asteroid models enables us to study the spin distribution in the asteroid population. The distribution of spins confirms previous findings that (i) small asteroids have poles clustered toward ecliptic poles, likely because of the YORP-induced spin evolution, (ii) asteroid migration due to the Yarkovsky effect depends on the spin orientation, and (iii) members of asteroid families have the sense of rotation correlated with their proper semimajor axis: over the age of the family, orbits of prograde rotators evolved, due to the Yarkovsky effect, to larger semimajor axes, while those of retrograde rotators drifted in the opposite direction.