  We present the results of the analysis of the GREAT (Galileo gravitational
Redshift test with Eccentric sATellites) experiment from SYRTE (Observatoire de
Paris), funded by the European Space Agency. An elliptic orbit induces a
periodic modulation of the fractional frequency difference between a ground
clock and the satellite clock, while the good stability of Galileo clocks
allows to test this periodic modulation to a high level of accuracy. Galileo
satellites GSAT0201 and GSAT0202, with their large eccentricity and on-board
H-maser clocks, are perfect candidates to perform this test. By analyzing 1008
days of eccentric Galileo satellites data we measure the fractional deviation
of the gravitational redshift from the prediction by general relativity to be
$(+0.19 \pm 2.48)\times10^{-5}$ at 1 sigma, improving the best previous test by
Gravity Probe A by a factor~5.6. Moreover, we apply the exact same analysis to
two almost circular Galileo satellites, in order to show the robustness of the
method. By analyzing 899 days of circular Galileo satellites data we measure
the fractional deviation of the gravitational redshift from the prediction by
general relativity to be $(+0.29 \pm 2.00)\times10^{-2}$ at 1 sigma.
