Recent earthquakes have demonstrated that monumental structures located in regions characterized by high seismic hazard are particularly sensitive to damage, stimulating a growing attention to the formulation of cost-effective and long-lasting methods for damage assessment. Generally, the evaluation of a healthy or damaged state is data-driven and it can be subjected to a large amount of uncertainty. In order to associate a damage symptom to a possible structural damage including all the uncertainties involved in the process, a Bayesian-based data fusion methodology is proposed. To this purpose, different sources of information are combined, such as dynamic structural properties extracted from monitoring data (natural frequencies and mode shapes), static response data (crack amplitudes) and visual inspections. More in depth, the proposed procedure comprises three fundamental steps: i) calibration of a finite element (FE) model, partitioned in well-thought-out macro-elements on the basis of engineering judgments and/or numerical simulations and, subsequently, construction of a tuned surrogate model considering pre-selected uncertain parameters as inputs, such as the Young's modulus, shear modulus, Poisson's ratio and mass density associated to each macro-element;   ii) solve the Bayesian-based inverse problem aimed at deriving the posterior statistics of the uncertain parameters over the space of the surrogate model's classes in a computational effective manner by using dynamic data; iii) adjust the posterior distribution on the basis of the information obtained from static data and visual inspections, i.e., data fusion. The suitability of the proposed approach is demonstrated via numerical simulations and 1-year of recorded data pertaining to a monumental palace, located in Gubbio (Italy) and named Consoli Palace, which has been monitored by the Authors since 2017 with an updating of the sensor network made in 2020. The monitoring system consists of an integrated sensor network deployed on the structure and composed by: a data acquisition system; twelve unidirectional accelerometers; four transducers; four thermocouples.