The generation of Synthetic Computed Tomography (sCT) images has become a pivotal methodology in modern clinical practice, particularly in the context of Radiotherapy (RT) treatment planning. The use of sCT enables the calculation of doses, pushing towards Magnetic Resonance Imaging (MRI) guided radiotherapy treatments. Moreover, with the introduction of MRI-Positron Emission Tomography (PET) hybrid scanners, the derivation of sCT from MRI can improve the attenuation correction of PET images. Deep learning methods for MRI-to-sCT have shown promising results, but their reliance on single-centre training dataset limits generalisation capabilities to diverse clinical settings. Moreover, creating centralised multicentre datasets may pose privacy concerns. To solve the issues, this study introduces FedSynthCT-Brain, a framework based on the Federated Learning (FL) paradigm for MRI-to-sCT in brain imaging. We reproduced a federation across four European and American centres using a U-Net-based model. The approach was implemented using data from centres belonging the federation and it was tested on an unseen dataset from a centre outside the federation. In the case of the unseen centre, the federated model achieved a median Mean Absolute Error (MAE) of 102.0 HU across 23 patients, with an interquartile range of 96.7-110.5 HU. The median (interquartile range) for the Structural Similarity Index (SSIM) and the Peak Signal to Noise Ratio (PNSR) were 0.89 (0.86-0.89) and 26.58 (25.52-27.42), respectively. The analysis of the results showed acceptable performances of the federated approach, thus highlighting the potential of FL to enhance MRI-to-sCT to improve generalisability and advancing safe and equitable clinical applications while fostering collaboration and preserving data privacy.