Smart phones are communication and entertainment tools with mental health consequences for heavy users. The study therefore examines the prevalence and relationship between depression, anxiety and smart phone addiction among young people in Nigeria. Using cross-sectional research design, a structured questionnaire comprising of demographic information, Smart phone Addiction Scale-Short Version (SAS-SV), Generalized Anxiety Disorder Scale (GAD-7) and Patient Health Questionnaire (PHQ-9) was used to collect data from 500 (51.6% females) respondents selected by quota technique, aged 16 to 32 years (X=21.95, SD= 2.88), at five higher institutions. Data was analyzes with descriptive statistics, correlation analysis and multiple regression analysis. Results showed 10.2% of the respondents manifested with probable smart phone addiction, 23.4% at the risk of smart phone addiction, 21.6% manifested with depression and 14.8% manifested with anxiety symptoms. There was significant relationship between addictive smart phone use and depression (r = 0.26, p < 0.01), anxiety(r = 0.23, p < 0.01), financial income level (r = 0.12, p < 0.01) and being married (r = -0.09, p < 0.05), but not with age and gender. Psychological predictors of smart phone addiction were depression (β=0.20, t=3.54, P<0.00), financial income level (β=0.14, t=3.12, P<0.01), marital status (β=-0.11, t=-2.40, P<0.05) and anxiety (β=0.11, t=1.98, P<0.05). All the independent variable jointly predict smart phone addiction at (R2= .10, F (6, 493) = 9.58, P<.00). The prevalence and positive relationship between depression, anxiety and smart phone addiction indicate a need to challenge these menace. Smart phone should be used moderated by users to reduce its adverse effects on mental health.