A hierarchical Bayesian model is applied to the Cosmicflows-3 catalog of galaxy distances in order to derive the peculiar velocity field and distribution of matter within z ∼ 0.054. The model assumes the ΛCDM model within the linear regime and includes the fit of the galaxy distances together with the underlying density field. By forward modeling the data, the method is able to mitigate biases inherent to peculiar velocity analyses, such as the Homogeneous Malmquist bias or the log-normal distribution of peculiar velocities. The statistical uncertainty on the recovered velocity field is about 150 km/s depending on the location, and we study systematics coming from the selection function and calibration of distance indicators. The resulting velocity field and related density fields recover the cosmography of the Local Universe which is presented in an unprecedented volume of universe 10 times larger than previously reached. This methodology open the doors to reconstruction of initial conditions for larger and more accurate constrained cosmological simulations. This work is also preparatory to larger peculiar velocity datasets coming from Wallaby, TAIPAN or LSST.