Gallic acid is a powerful antioxidant with multiple therapeutic applications, usually obtained from the acidic hydrolysis of tannins produced by many plants. As this process generates a considerable amount of toxic waste, the use of tannases or tannase-producing microorganisms has become a greener alternative over the last years. However, their high costs still impose some barriers for industrial scalability, requiring solutions that could be both greener and cost-effective. Since Pseudomonas putida KT2440 is a powerful degrader of gallic acid, its metabolism offers pathways that can be engineered to produce it from cheap and renewable carbon sources, such as the crude glycerol generated in biodiesel units. In this study, a synthetic operon with the heterologous genes aroG4, quiC and pobA* was developed and expressed in P. putida, based on an in silico analysis of possible metabolic routes, resulting in no production. Then, the sequences pcaHG and galTAPR were deleted from the genome of this strain to avoid the degradation of gallic acid and its main intermediate, the protocatechuic acid. This mutant was transformed with the vector containing the synthetic operon and was finally able to convert glycerol into gallic acid. Production assays in shaker showed a final concentration of 346.7 ± 0.004 mg L−1 gallic acid after 72 h.