  The excess of $\gamma$ rays in the data measured by Fermi-LAT from the
Galactic center region is one of the most intriguing mysteries in Astroparticle
Physics. This Galactic center excess (GCE), has been measured with respect to
different interstellar emission models (IEMs), source catalogs, data selections
and techniques. Although several proposed interpretations have appeared in the
literature, there are not firm conclusions as to its origin. The main
difficulty in solving this puzzle lies in modeling a region of such complexity
and thus precisely measuring the characteristics of the GCE. In this paper, we
use 11 years of Fermi-LAT data, state of the art IEMs, and the newest 4FGL
source catalog to provide precise measurements of the energy spectrum, spatial
morphology, position, and sphericity of the GCE. We find that the GCE has a
spectrum which is peaked at a few GeV and is well fit with a log-parabola. The
normalization of the spectrum changes by roughly $60\%$ when using different
IEMs, data selections and analysis techniques. The spatial distribution of the
GCE is compatible with a dark matter (DM) template produced with a generalized
NFW density profile with slope $\gamma = 1.2-1.3$. No energy evolution is
measured for the GCE morphology between $0.6-30$ GeV at a level larger than
$10\%$ of the $\gamma$ average value, which is 1.25. The analysis of the GCE
modeled with a DM template divided into quadrants shows that the spectrum and
spatial morphology of the GCE is similar in different regions around the
Galactic center. Finally, the GCE centroid is compatible with the Galactic
center, with best-fit position between
$l=[-0.3^{\circ},0.0^{\circ}],b=[-0.1^{\circ},0.0^{\circ}]$, and it is
compatible with a spherical symmetric morphology. In particular, fitting the DM
spatial profile with an ellipsoid gives a major-to-minor axis ratio between
0.8-1.2.
