Social norms towards smoking are a key concept in tobacco control policy and research. However, the influence and strength of different types of social norms on youth smoking uptake is unclear. This study aimed to examine, quantify and compare evidence of the longitudinal associations between different types of social norms towards smoking and youth smoking uptake (initiation and escalation). Systematic review searching four databases (MEDLINE, EMBASE, PsycInfo, CINAHL) from January 1998 to October 2020. Evidence synthesis via narrative review, meta-analysis pooling unadjusted associations (initiation only, due to heterogeneity in escalation outcomes) and meta-regression comparing effect sizes by norm type and study characteristics. Studies included observational prospective cohort studies using survey methodology with youth aged ≤24years. Measurements included longitudinal associations between descriptive norms (perceived smoking behaviour) and injunctive norms (perceived approval/disapproval of smoking) among social network(s) and subsequent smoking initiation or escalation. Thirty articles were identified. In the narrative review, smoking initiation (but not escalation) was consistently predicted by two norms: parental and close friend smoking. Associations between smoking uptake and other descriptive norms (smoking among siblings, family/household, partner, peers, adults) and all injunctive norms (perceived approval of smoking among parents, siblings, close friends/peers, partner, teachers, people important to you, the public) were less consistent or inconclusive. In the meta-analysis pooling unadjusted associations, 17 articles were included (n=27 767). Smoking initiation was predicted by the following descriptive norms: smoking among parents [Odds Ratio (OR)=1.88, 95% Confidence Interval (CI)=1.56-2.28], close friends (OR=2.53, 95% CI=1.99-3.23), siblings (OR=2.44, 95% CI=1.93-3.08), family/household (OR=1.55, 95% CI=1.36-1.76) and adults (OR=1.34, 95% CI=1.02-1.75), but not peers (OR=1.14, 95% CI=0.92-1.42). Smoking initiation was also predicted by two injunctive norms, perceived approval of smoking among parents (OR=1.74, 95% CI=1.27-2.38) and the public (OR=4.57, 95% CI=3.21-6.49), but not close friends/peers (OR=2.36, 95% CI=0.86-6.53) or people important to the individual (OR=1.24, 95% CI=0.98-1.58). In this systematic review (narrative and meta-analysis), descriptive norms of parents' and close friends' smoking behaviour appeared to be consistent predictors of youth smoking initiation, more so than the descriptive norms of more distal social networks and injunctive norms.