Call detail records (CDR) collected by mobile phone network providers have been largely used to model and analyze human-centric mobility. Despite their potential, they are limited in terms of both spatial and temporal accuracy thus being unable to capture detailed human mobility information. Network Signaling Data (NSD) represent a much richer source of spatio-temporal information currently collected by network providers, but mostly unexploited for fine-grained reconstruction of human-centric trajectories. In this paper, we present TRANSIT, TRAjectory inference from Network SIgnaling daTa, a novel framework capable of proceessing NSD to accurately distinguish mobility phases from stationary activities for individual mobile devices, and reconstruct, at scale, fine-grained human mobility trajectories, by exploiting the inherent recurrence of human mobility and the higher sampling rate of NSD. The validation on a ground-truth dataset of GPS trajectories showcases the superior performance of TRANSIT (80% precision and 96% recall) with respect to state-of-the-art solutions in the identification of movement periods, as well as an average 190 m spatial accuracy in the estimation of the trajectories. We also leverage TRANSIT to process a unique large-scale NSD dataset of more than 10 millions of individuals and perform an exploratory analysis of city-wide transport mode shares, recurrent commuting paths, urban attractivity and analysis of mobility flows.