The progressive increase in infections caused by multidrug-resistant (MDR) Gram-negative bacteria and the emergence of resistance to last-resort antimicrobial drugs in recent years necessitate the development of new therapeutic strategies. This study was conducted to obtain nanostructured antimicrobials by conjugating colistin (COL) and meropenem (MEM) antibiotics with biosynthesized silver nanoparticles (bio-AgNPs) via the green synthesis method using Rosa damascena extract, and to investigate the antibacterial and antibiofilm activity of these nanostructures against Escherichia coli and Klebsiella pneumoniae strains. Ultraviolet–visible spectrophotometry, high-resolution-transmission electron microscopy, atomic force microscopy, X-ray diffraction, and Fourier transform-infrared spectroscopy analyses were performed to determine the physical and chemical properties of synthesized bio-AgNPs, COL@bio-AgNPs, MEM@bio-AgNPs, and COL&MEM@bio-AgNPs. The minimum inhibitory concentration (MIC) and minimum bactericidal concentration of nanoparticles were determined on standard and MDR clinical strains. The antibiofilm efficacy and cytotoxic effect of nanoparticles were evaluated by the crystal violet dye method and 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide dye method, respectively. The characterization analyses demonstrated that the synthesized nanoparticles had crystal structure and spherical morphology (5.6–30.2 nm in size). Antibiotic conjugated nanoparticles exhibited better antimicrobial activity and lower MIC values (0.125–4 µg/mL) on the tested strains compared to free antibiotics, and MIC values were decreased up to 1024-fold (p < 0.05). Antibiotic conjugated nanoparticles were found to be more effective in biofilm eradication than free antibiotics and bio-AgNPs and had a less inhibitory effect on peripheral blood mononuclear cell viability. The findings revealed that antibiotic-conjugated nanoparticles have the potential to be used as an effective antimicrobial drug against MDR E. coli and K. pneumoniae strains.