This study investigated the associations between two common recreational screen activities and the psychological wellbeing of adolescents, and whether this association was mediated by sleep duration or physical activity frequency. This study used nationally representative cross-sectional survey data from 2946 adolescents (mean age 16.9 [0.38] years; 49% female) in the Longitudinal Study of Australian Children (LSAC). Adolescents provided information on daily time spent for each of the following: playing electronic games and watching television, time of sleep onset and wakeup, and number of days/week doing ≥60 min/day of physical activity. Psychological wellbeing was assessed by the Strengths and Difficulties Questionnaire (SDQ). Generalized estimating equations were used to examine the associations, and a contemporary multiple mediation analysis was used to examine the mediation effects. One fifth (20%) of adolescents were categorized as having poor wellbeing (SDQ total ≥17) with a significant sex difference (males: 16%; females: 24%; p < 0.001). Playing electronic games was inversely associated with psychological wellbeing for both male and female adolescents (p < 0.001). Watching television was inversely associated with psychological wellbeing for female adolescents (p < 0.001). Sleep duration and physical activity frequency were found to partially mediate the relationships between playing electronic games and the psychological wellbeing of male and female adolescents. Physical activity frequency partially mediated the association between television watching and wellbeing among female adolescents. Longitudinal studies are required to determine the causal pathway between screen-based activities and the wellbeing of adolescents, and to inform intervention strategies.