Background The aim of this study was to identify factors associated with continuity of medication administration following transitions-of-care from hospitals to residential aged-care facilities (RACFs). Methods This was a prospective, observational study of randomly selected patients discharged to an RACF from hospitals within four public health services in Victoria, Australia. Data were collected from hospital medical records and structured telephone interviews with RACF nurses post-discharge. Multivariable regression analysis using a modified Poisson model with generalised estimating equations was performed to estimate adjusted relative risks (RRs) and confidence intervals (CIs). The dependent variable was missed or significantly delayed medication doses at RACFs 24-h post-discharge. Results Nurses for 397 patients at 78 RACFs were interviewed. Ninety (22.7%) patients had one or more missed or significantly delayed doses. There was lower risk of missed/delayed doses when the hospital supplied discharge medications (RR 0.53, 95% CI 0.33–0.85), community pharmacy delivered repackaged medications on the day-of-discharge (RR 0.48, 95% CI 0.30–0.76), the hospital provided an interim medication administration chart (RR 0.63, 95% CI 0.46–0.85), and there was more time between discharge and the first post-discharge medication dose-time (RR 0.91, 95% CI 0.86–0.96 for each additional hour). There was higher risk of missed/delayed doses when there were multiple medication changes in hospital (RR 1.05, 95% CI 1.04–1.07 for each additional change) and when the RACF medication chart was prepared/updated by a GP or locum on the day-of-discharge (RR 1.38, 95% CI 1.23–1.56). Conclusions Missed and significantly delayed doses were less likely when hospitals provided discharge medications and an interim medication administration chart, and when community pharmacies delivered repackaged medications on day-of-discharge.