Chromosomally encoded low membrane permeability and highly efficient efflux systems are major mechanisms by which Pseudomonas aeruginosa evades antibiotic actions. Our previous reports have shown that amphiphilic tobramycin-fluoroquinolone hybrids can enhance efficacy of fluoroquinolone antibiotics against multidrug-resistant (MDR) P. aeruginosa isolates. Herein, we report on a novel class of tobramycin-lysine conjugates containing an optimized amphiphilic tobramycin-C12 tether that sensitize Gram-negative bacteria to legacy antibiotics. Combination studies indicate the ability of these conjugates to synergize rifampicin and minocycline against MDR and extensively drug resistant (XDR) P. aeruginosa isolates and enhance efficacy of both antibiotics in the Galleria mellonella larvae in vivo infection model. Mode of action studies indicate that the amphiphilic tobramycin-lysine adjuvants enhance outer membrane cell penetration and affect the proton motive force, which energizes efflux pumps. Overall, this study provides a strategy for generating effective antibiotic adjuvants that overcome resistance of rifampicin and minocycline in MDR and XDR Gram-negative bacteria including P. aeruginosa.