The intensive care unit (ICU) comprises a complex hospital environment, where decisions made by clinicians have a high level of risk for the patients' lives. A comprehensive care pathway must then be followed to reduce p complications. Uncertain, competing and unplanned aspects within this environment increase the difficulty in uniformly implementing the care pathway. Readmission contributes to this pathway's difficulty, occurring when patients are admitted again to the ICU in a short timeframe, resulting in high mortality rates and high resource utilisation. Several works have tried to predict readmission through patients' medical information. Although they have some level of success while predicting readmission, those works do not properly assess, characterise and understand readmission prediction. This work proposes a standardised and explainable machine learning pipeline to model patient readmission on a multicentric database (i.e., the eICU cohort with 166,355 patients, 200,859 admissions and 6,021 readmissions) while validating it on monocentric (i.e., the MIMIC IV cohort with 382,278 patients, 523,740 admissions and 5,984 readmissions) and multicentric settings. Our machine learning pipeline achieved predictive performance in terms of the area of the receiver operating characteristic curve (AUC) up to 0.7 with a Random Forest classification model, yielding an overall good calibration and consistency on validation sets. From explanations provided by the constructed models, we could also derive a set of insightful conclusions, primarily on variables related to vital signs and blood tests (e.g., albumin, blood urea nitrogen and hemoglobin levels), demographics (e.g., age, and admission height and weight), and ICU-associated variables (e.g., unit type). These insights provide an invaluable source of information during clinicians' decision-making while discharging ICU patients.