Background Acute respiratory infection (ARI) and diarrhoea are the leading causes of childhood morbidity and mortality in Ethiopia. Understanding the associations between infant and young child feeding (IYCF) and ARI and diarrhoea can inform IYCF policy interventions and advocacy in Ethiopia. This study aimed to investigate the relationship between IYCF practices and ARI and diarrhoea in Ethiopian children. Methods This study used the Ethiopia Demographic and Health Survey (EDHS) data for the years 2000 (n = 3680), 2005 (n = 3528), 2011 (n = 4037), and 2016 (n = 3861). The association between IYCF practices and (i) ARI and (ii) diarrhoea were investigated using propensity score matching and multivariable logistic regression models. The IYCF practices include early initiation of breastfeeding, exclusive breastfeeding (EBF), predominant breastfeeding, introduction of complementary foods, continued breastfeeding at two years and bottle feeding. Results Infants and young children who were breastfed within 1-hour of birth and those who were exclusively breastfed had a lower prevalence of ARI. Infants who were exclusively and predominantly breastfed had a lower prevalence of diarrhoea. Early initiation of breastfeeding (Odds ratio [OR]: 0.81; 95% confidence interval [CI]: 0.72, 0.92) and EBF (OR: 0.65; 95% CI: 0.51, 0.83) were associated with lower risk of ARI. Bottle-fed children had higher odds of ARI (OR: 1.36; 95% CI: 1.10, 1.68). Early initiation of breastfeeding and EBF were associated with lower odds of diarrhoea (OR: 0.88; 95% CI: 0.79, 0.94 for Early initiation of breastfeeding and OR: 0.51; 95% CI: 0.39, 0.65 for EBF). Infants who were predominantly breastfed were less likely to experience diarrhoea (OR: 0.69; 95% CI: 0.53, 0.89). Conclusion The recommended best practices for preventing ARI and diarrhoeal diseases in infants and young children namely: the early initiation of breastfeeding, EBF and avoidance of bottle feeding should be institutionalized and scale-up in Ethiopia as part of implementation science approach to cover the know-do-gaps.