The extraction of antioxidants from plant biomass is of high interest and it requires processing conditions that preserve the bioactivity of these compounds. The optimization of the solvent extraction of antioxidants from the leaves of Eucalyptus globulus is a key point for its exploitation at industrial scale. In this work, the Box-Behnken experimental design was used to evaluate the effects of three independent variables (temperature, time and ratio of ethanol/water) on the response of extraction yield, total phenolic content (TPC), total flavonoid content (TFC) and antioxidant capacity. Under optimal extraction conditions, the response values were 32.7% for extraction yield, 92.9 mg GAE/g dried leaf and 53.7 mg RE/g dried leaf for TPC and TFC, respectively, with antioxidant levels of 205.4, 363.4 and 185.2 mg TE/g dried leaf as determined by the DPPH, ABTS and FRAP methods, respectively. The extract obtained under optimal conditions was characterized by TGA, FTIR and Py-GC/MS. The Py-GC/MS analysis revealed that the main components found in the extract are sesquiterpenes, eudesmol, γ-eudesmol and globulol. Additionally, the antimicrobial activity of the extract was tested against several pathogens by showing capability to inhibit their growth. Therefore, the extract from E. globulus leaves could be used as a “natural” bioactive agent in several industrial applications.