* Confirmation of invasive species eradication following management programs is typically determined by waiting an arbitrary period before determining success or failure based upon the then obvious presence or absence of the target species. Rapid eradication assessment could be achieved more expediently by applying statistical models of the probability of detecting survivors and their offspring, using a grid of detection devices, for a given set of biological and monitoring parameters. * We simulate estimation of the probability of eradication for invasive rodents on islands across a range of monitoring parameters to guide managers on the optimal values, diminishing returns, and trade-offs in monitoring to achieve a given level of confidence in successful eradication. * We found that monitoring an island for survivors over 15–20 nights is optimal and that waiting longer than a year before commencing monitoring has a negligible impact on the estimated probability of success. The spacing between detection devices has a considerable influence on the estimated probability of success but only when it is <60 m. * Intrinsic biological parameters of the target species have a substantial impact on confirming the probability of success but validated field data are lacking to reliably incorporate these in current rapid eradication assessment models. * We present case studies demonstrating cost savings of at least 5% to managers when applying rapid eradication assessment to the eradication of house mice Mus musculus from Isla Pájaros and Isla Muertos in Arrecife Alacranes (Scorpion Reef) Mexico, and implement the rapid eradication assessment model in an HTML GUI interface for eradication managers (www.rea.is). * Synthesis and applications. Rapid eradication assessment (REA) is a powerful tool for managers to design optimal invasive species eradication monitoring programs. We recommend island eradication managers routinely implement REA on small islands for the demonstrated cost savings and to accelerate eradication confirmation, ultimately facilitating island restoration.