We provide a purely dynamical global map of the non-axisymmetric structure of the Milky Way disk. For this, we exploited the information contained within the in-plane motions of disk stars from Gaia DR3 to adjust a model of the Galactic potential, including a detailed parametric form for the bar and spiral arms. We explored the parameter space of the non-axisymmetric components with the backward integration method, first adjusting the bar model to selected peaks of the stellar velocity distribution in the solar neighborhood, and then adjusting the amplitude, phase, pitch angle, and pattern speed of spiral arms to the median radial velocity as a function of position within the disk. We checked a posteriori that our solution also qualitatively reproduces various other features of the global non-axisymmetric phase-space distribution, including most moving groups and phase-space ridges, despite those not being primarily used in the adjustment. This fiducial model has a bar with a pattern speed of 37 km s−1 kpc−1 and two spiral modes that are twoarmed and three-armed, respectively. The two-armed spiral mode has a ~25% local contrast surface density and a low pattern speed of 13.1 km s−1 kpc−1, and matches the location of the Crux-Scutum, Local, and Outer arm segments. The three-armed spiral mode has a ~9% local contrast density, a slightly higher pattern speed of 16.4 km s−1 kpc−1, and matches the location of the Carina-Sagittarius and Perseus arm segments. The Galactic bar, with a higher pattern speed than both spiral modes, has recently disconnected from those two arms. The fiducial non-axisymmetric potential presented in this paper, reproducing most non-axisymmetric signatures detected in the stellar kinematics of the Milky Way disk, can henceforth be used to confidently integrate orbits within the Galactic plane.