We present an analysis of Multi Unit Spectroscopic Explorer (MUSE) observations obtained on the massive Frontier Fields (FFs) cluster A2744. This new data set covers the entire multiply imaged region around the cluster core. The combined catalogue consists of 514 spectroscopic redshifts (with 414 new identifications). We use this redshift information to perform a strong-lensing analysis revising multiple images previously found in the deep FF images, and add three new MUSE-detected multiply imaged systems with no obvious Hubble Space Telescope counterpart. The combined strong-lensing constraints include a total of 60 systems producing 188 images altogether, out of which 29 systems and 83 images are spectroscopically confirmed, making A2744 one of the most well-constrained clusters to date. Thanks to the large amount of spectroscopic redshifts, we model the influence of substructures at larger radii, using a parametrization including two cluster-scale components in the cluster core and several group scale in the outskirts. The resulting model accurately reproduces all the spectroscopic multiple systems, reaching an rms of 0.67-arcsec in the image plane. The large number of MUSE spectroscopic redshifts gives us a robust model, which we estimate reduces the systematic uncertainty on the 2D mass distribution by up to ~2.5 times the statistical uncertainty in the cluster core. In addition, from a combination of the parametrization and the set of constraints, we estimate the relative systematic uncertainty to be up to 9 per cent at 200kpc.