Executive functions and psychosocial health during childhood are positively associated with health and developmental outcomes into adulthood. Electronic media use has been reported to adversely affect health and development in children; however, what remains unclear is whether contemporary media behaviors, such as electronic application (app) use, exerts similar effects on health and development. We investigated the associations of electronic media use (program viewing and app use) with cognitive and psychosocial development in preschoolers. Parents of preschool children (n = 247, 4.2 ± 0.6 years) reported the time their child spent using electronic media. Direct assessment of the children’s executive functions (working memory, inhibition, and shifting) and educator-reported psychosocial difficulties were also collected. Associations were examined using linear regression adjustments for covariates and preschool clustering. Small, but significant, negative associations were observed for total electronic media use (b = −0.001; 95% CI: −0.003, −0.000; p = 0.026) and program viewing (b = −0.002; 95% CI: −0.003, −0.000; p = 0.033) with children’s visual–spatial working memory. However, high-dose app users demonstrated higher phonological working memory scores compared to non-users (MD = 0.31; 95% CI: 0.04, 0.58; p = 0.025). Similarly, compared to non-users, low-dose app users displayed statistically significantly fewer total difficulties (MD = −1.67; 95% CI: −3.31, −0.02; p = 0.047). No associations were evident for high-dose app users and the remaining outcomes. The results may suggest that attempts to reduce program viewing while promoting moderate levels of app use may exert positive influences on children’s executive functions and psychosocial development.