History matching (HM) is a complex process that aims to increase the reliability of reservoir simulation models. HM is an inverse problem with multiple solutions that calls for a probabilistic approach. When observed data are integrated with sampling methods, uncertainty can be reduced by updating the probability density function (pdf) of the attributes. This work presents a practical methodology to systematically reduce uncertainties in a multi-objective probabilistic assisted history matching, integrating well and 4D seismic data (4DS) quantitatively. The pdf update goes through an iterative process. The pdf of the current iteration is combined with the pdf generated using the best-matched models to generate the posterior pdf. The multiple local objective functions (OF) are evaluated independently, allowing the identification of OFs that indicate the requirement of re-parameterization. This quantitative process was applied in two phases: (I) using only well data to constrain the models; (II) adding 4DS data. The methodology was successfully validated against a benchmark case of medium complexity, with the history-production data generated at fine scale (reference model). The proposed methodology reduced uncertainties for the majority of attributes, achieving the highest probable levels similar to those of the reference values. The identification of objective functions that restricts the match allowed improving of the parameterization employed, by locally adding probabilistic perturbations to the petrophysical realizations. The method efficiently achieved multiple matched simulation models, with all (87) local objective functions within the defined tolerance range. Each iteration increased the number of matched models, demonstrating good convergence. The uncertainties were reduced gradually, avoiding premature level elimination (minimizing convergence at an incorrect solution). In both phases, the matched simulation models presented similar production forecasts to the reference model. The 4D seismic data were included regionally with an acceptable increase in computation time. The quantitative incorporation of 4D seismic data generated models that forecasted production with less variability than models generated without 4DS data. This was expected as for this study, 4D seismic data provided perfect information.