Studies on sleep and psychological functions have predominantly focused on the negative consequences of poor sleep. Little is known about whether and how sleep is associated with the positive aspects of psychological well-being that fosters healthy development. This study investigated (1) the sleep patterns across grades from Primary 4 to Secondary 6, (2) the associations of sleep variables with self-perceived strengths and difficulties, and positive well-being in terms of hope and happiness, and (3) the mediating role of emotional symptoms in the link between sleep and hope and happiness. A sample of 2,804 Chinese students (aged 9–15, 46% male) from local primary and secondary schools in Hong Kong completed questionnaires regarding their sleep, hope and happiness, and strengths and difficulties. Sleep quality was associated with higher levels of hope and happiness both directly and indirectly via less emotional symptoms, which fully mediated the relationship between sleep sufficiency and hope and happiness. The importance of sleep health for positive well-being of children and teens warrants further research and clinical attention as well as promotion of community awareness, given the potential benefits of sleep for psychosocial outcomes that are fundamental to optimal growth.