Consumers are driving food production toward the use of natural preservatives and minimal processing technologies. Green tea extract (GTE) at low concentration could be combined with high pressure processing (HPP) for reduced treatment times and quality impact on foods in a hurdle concept for synergistic effects on foodborne viral pathogens, specifically human norovirus and hepatitis A virus (HAV). Viral inactivation by HPP (at 300, 400, and 500 MPa for 5 min) combined with 3.3 mg/mL aged-GTE was initially evaluated in buffer (PBS) against murine norovirus (MNV), a culturable human norovirus surrogate, and HAV. Furthermore, human norovirus inactivation was evaluated by the novel human intestinal enteroid system (HIE) and a capsid integrity binding assay (ISC-RT-qPCR). HPP treatment completely inhibits human norovirus GII.4 infectivity when applied at 500 MPa alone and at 400 MPa combined with aged-GTE. Additional experiments investigated the reduction of MNV and HAV infectivity in apple and horchata juices exposed to combined aged-GTE and HPP treatments. Results demonstrated that the addition of aged-GTE to the juices exposed to HPP significantly inactivated MNV and HAV at reduced holding pressure time. This synergistic effect of aged-GTE combined with HPP treatments represents a hurdle technology that could be exploited as a control measure to improve the food safety of beverages.