Antibiotic resistance increases the likelihood of death from infection by common pathogens such as Escherichia coli and Klebsiella pneumoniae in developed and developing countries alike. Most important modern antibiotic resistance genes spread between such species on self-transmissible (conjugative) plasmids. These plasmids are traditionally grouped on the basis of replicon incompatibility (Inc), which prevents coexistence of related plasmids in the same cell. These plasmids also use post-segregational killing (`addiction') systems, which poison any bacterial cells that lose the addictive plasmid, to guarantee their own survival. This study demonstrates that plasmid incompatibilities and addiction systems can be exploited to achieve the safe and complete eradication of antibiotic resistance from bacteria in vitro and in the mouse gut. Conjugative `interference plasmids' were constructed by specifically deleting toxin and antibiotic resistance genes from target plasmids. These interference plasmids efficiently cured the corresponding antibiotic resistant target plasmid from different Enterobacteriaceae in vitro and restored antibiotic susceptibility in vivo to all bacterial populations into which plasmid-mediated resistance had spread. This approach might allow eradication of emergent or established populations of resistance plasmids in individuals at risk of severe sepsis, enabling subsequent use of less toxic and/or more effective antibiotics than would otherwise be possible, if sepsis develops. The generalisability of this approach and its potential applications in bioremediation of animal and environmental microbiomes should now be systematically explored.