Background Cross-sectional studies have found a relationship between social media use and depression and anxiety in young people. However, few longitudinal studies using representative data and mediation analysis have been conducted to understand the causal pathways of this relationship. Objective This study aims to examine the longitudinal relationship between social media use and young people’s mental health and the role of self-esteem and social connectedness as potential mediators. Methods The sample included 3228 participants who were 10- to 15-year-olds from Understanding Society (2009-2019), a UK longitudinal household survey. The number of hours spent on social media was measured on a 5-point scale from “none” to “7 or more hours” at the ages of 12-13 years. Self-esteem and social connectedness (number of friends and happiness with friendships) were measured at the ages of 13-14 years. Mental health problems measured by the Strengths and Difficulties Questionnaire were assessed at the ages of 14-15 years. Covariates included demographic and household variables. Unadjusted and adjusted multilevel linear regression models were used to estimate the association between social media use and mental health. We used path analysis with structural equation modeling to investigate the mediation pathways. Results In adjusted analysis, there was a nonsignificant linear trend showing that more time spent on social media was related to poorer mental health 2 years later (n=2603, β=.21, 95% CI −0.43 to 0.84; P=.52). In an unadjusted path analysis, 68% of the effect of social media use on mental health was mediated by self-esteem (indirect effect, n=2569, β=.70, 95% CI 0.15-1.30; P=.02). This effect was attenuated in the adjusted analysis, and it was found that self-esteem was no longer a significant mediator (indirect effect, n=2316, β=.24, 95% CI −0.12 to 0.66; P=.22). We did not find evidence that the association between social media and mental health was mediated by social connectedness. Similar results were found in imputed data. Conclusions There was little evidence to suggest that more time spent on social media was associated with later mental health problems in UK adolescents. This study shows the importance of longitudinal studies to examine this relationship and suggests that prevention strategies and interventions to improve mental health associated with social media use could consider the role of factors like self-esteem.