Endophytic fungi can inherently establish mutual relationships with host plants while also synthesizing similar and enhanced bioactive compounds as the host. The focus of this study was to investigate the exploitable antibacterial and antioxidant bioactive compounds produced by fungal endophytes from selected medicinal plants. According to standard procedures, 15 fungi were isolated from leaf segments of Cola acuminata, Bambusa vulgaris, and Elaeis guineensis. By solid-state fermentation using a rice medium, fungal secondary metabolites were extracted using ethyl acetate. About six human pathogens, including Bacillus subtilis, Staphylococcus aureus, Pseudomonas aeruginosa, Escherichia coli, Aspergillus niger, and Candida albicans, the antibacterial properties of the crude extracts were evaluated using the agar diffusion assay. Except for E. coli, all endophytic fungal extracts showed promising inhibitory effects against all test isolates. The free radical scavenging activity was estimated using the 1, 1-diphenyl-2-picrylhydrazyl (DPPH) free radical assay, and the bioactive constituents were analyzed using gas chromatography-mass spectrometry (GC-MS). The metabolites of the endophytic fungi also showed good antioxidant activity. Three of the fungi with the best activities were identified as L. theobromae (Ca1), C. lunata (Bv4), and C. lunata (Eg7), using molecular techniques (ITS region). GC-MS analysis of these fungal extracts revealed the presence of 17 antimicrobial and antioxidant compounds such as 2,4-di-tert-butylphenol, p-Cymene, γ-Terpinene, β-Bisabolene, and hexadecanoic acid. Endophytic fungi associated with Nigerian medicinal plants are potentially rich sources of antibacterial and antioxidant compounds that could be exploited for drug discovery.