Childhood linear growth faltering remains a major public health concern in Nepal. Nevertheless, over the past 20 years, Nepal sustained one of the most rapid reductions in the prevalence of stunting worldwide. First, our study analysed the trends in height-for-age z-score (HAZ), stunting prevalence, and available nutrition-sensitive and nutrition-specific determinants of linear growth faltering in under-three children across Nepal's Family Health Survey 1996 and Nepal's Demographic and Health Surveys 2001, 2006, 2011, and 2016. Second, we constructed pooled multivariable linear regression models and decomposed the contributions of our time-variant determinants on the predicted changes in HAZ and stunting over the past two decades. Our findings indicate substantial improvements in HAZ (38.5%) and reductions in stunting (-42.6%) and severe stunting prevalence (-63.9%) in Nepalese children aged 0-35 months. We also report that the increment in HAZ, across the 1996-2016 period, was significantly associated (confounder-adjusted p < .05) with household asset index, maternal and paternal years of education, maternal body mass index and height, basic child vaccinations, preceding birth interval, childbirth in a medical facility, and prenatal doctor visits. Furthermore, our quantitative decomposition of HAZ identified advances in utilisation of health care and related services (31.7% of predicted change), household wealth accumulation (25%), parental education (21.7%), and maternal nutrition (8.3%) as key drivers of the long-term and sustained progress against child linear growth deficits. Our research reiterates the multifactorial nature of chronic child undernutrition and the need for coherent multisectoral nutrition-sensitive and nutrition-specific strategies at national scale to further improve linear growth in Nepal. [Correction added on 6 November 2020, after first online publication: in abstract, the citation year in the fourth sentence has been changed from '2001' to '2011'.]. © 2020 The Authors. Maternal & Child Nutrition published by John Wiley & Sons, Ltd.