A full understanding of the dynamics of mountain ranges such as the Alps requires the integration of available geological and geophysical knowledge into a lithospheric-scale 3-D geological model. As a first stage in the construction of this geo-model, we derive a new 3-D shear wave velocity model of the Alpine region, with a spatial resolution of a few tens of kilometres, making it possible to compare with geological maps. We use four years of continuous vertical-component seismic noise records to compute noise correlations between more than 950 permanent broad-band stations complemented by similar to 600 temporary stations from the AlpArray sea-land seismic network and the Cifalps and EASI linear arrays. A specific pre-processing is applied to records of ocean-bottom seismometers in the Liguro-Provencal basin to clean them from instrumental and oceanic noises. We first perform a 2-D transdimensional inversion of the traveltimes of Rayleigh waves to compute group-velocity maps from 4 to 150 s. The data noise level treated as an unknown parameter is determined with a Hierarchical Bayes method. A Fast Marching Eikonal solver is used to update ray path geometries during the inversion. We use next the group-velocity maps and their uncertainties to derive a 3-D probabilistic V-s model. The probability distributions of V-s at depth and the probability of presence of an interface are estimated at each location by exploring a set of 130 million synthetic four-layer 1-D V-s models. The obtained probabilistic model is refined using a linearized inversion. Throughout the inversion for V-s, we include the water column where necessary. Our V-s model highlights strong along-strike changes of the lithospheric structure, particularly in the subduction complex between the European and Adriatic plates. In the South-Western Alps, our model confirms the existence of a low-velocity structure at 50 - 80 km depth in the continuation of the European continental crust beneath the subduction wedge. This deep low-velocity anomaly progressively disappears towards the North-Western and Central Alps. The European crust includes lower crustal low-velocity zones and a Moho jump of similar to 8 - 12 km beneath the western boundary of the External Crystalline Massifs of the North-Western Alps. The striking fit between our V-s model and the receiver function migrated depth section along the Cifalps profile documents the reliability of the V-s model. In light of this reliability and with the aim to building a 3-D geological model, we re-examine the geological structures highlighted along the Cifalps profile.