Objective To compare induction of labour at 41 weeks with expectant management until 42 weeks in low risk women. Design Open label, randomised controlled non-inferiority trial. Setting 123 primary care midwifery practices and 45 hospitals (secondary care) in the Netherlands, 2012-16. Participants 1801 low risk women with an uncomplicated singleton pregnancy: randomised to induction (n=900) or to expectant management until 42 weeks (n=901). Interventions Induction at 41 weeks or expectant management until 42 weeks with induction if necessary. Primary outcome measures Primary outcome was a composite of perinatal mortality and neonatal morbidity (Apgar score <7 at five minutes, arterial pH <7.05, meconium aspiration syndrome, plexus brachialis injury, intracranial haemorrhage, and admission to a neonatal intensive care unit (NICU). Secondary outcomes included maternal outcomes and mode of delivery. The null hypothesis that expectant management is inferior to induction was tested with a non-inferiority margin of 2%. Results Median gestational age at delivery was 41 weeks+0 days (interquartile range 41 weeks+0 days-41 weeks+1 day) for the induction group and 41 weeks+2 days (41 weeks+0 days-41 weeks+5 days) for the expectant management group. The primary outcome was analysed for both the intention-to-treat population and the per protocol population. In the induction group, 15/900 (1.7%) women had an adverse perinatal outcome versus 28/901 (3.1%) in the expectant management group (absolute risk difference a '1.4%, 95% confidence interval a '2.9% to 0.0%, P=0.22 for non-inferiority). 11 (1.2%) infants in the induction group and 23 (2.6%) in the expectant management group had an Apgar score <7 at five minutes (relative risk (RR) 0.48, 95% CI 0.23 to 0.98). No infants in the induction group and three (0.3%) in the expectant management group had an Apgar score <4 at five minutes. One fetal death (0.1%) occurred in the induction group and two (0.2%) in the expectant management group. No neonatal deaths occurred. 3 (0.3%) neonates in the induction group versus 8 (0.9%) in the expectant management group were admitted to an NICU (RR 0.38, 95% CI 0.10 to 1.41). No significant difference was found in composite adverse maternal outcomes (induction n=122 (13.6%) v expectant management n=102 (11.3%)) or in caesarean section rate (both groups n=97 (10.8%)). Conclusions This study could not show non-inferiority of expectant management compared with induction of labour in women with uncomplicated pregnancies at 41 weeks; instead a significant difference of 1.4% was found for risk of adverse perinatal outcomes in favour of induction, although the chances of a good perinatal outcome were high with both strategies and the incidence of perinatal mortality, Apgar score <4 at five minutes, and NICU admission low. Trial registration Netherlands Trial Register NTR3431.