: The increasing integration of digital technologies into daily life, particularly during the COVID-19 pandemic, has raised concerns about internet and social media addictions and their potential impact on mental health. This study aimed to examine the prevalence of internet and social media addictions among adults in Cyprus in the post-pandemic period and explore their relationship with demographic characteristics, mental well-being (i.e., depression, anxiety, and stress), and self-esteem. Participants included 502 adults from Cyprus recruited using the convenience and snowball sampling methods. The data were collected via an internet-based questionnaire that examined participants’ levels of internet addiction, social media addiction, mental well-being, and self-esteem. The results suggest that (a) while the prevalence of severe addiction was low for both internet and social media addictions, approximately one-third of participants exhibited mild to moderate levels of addiction; (b) younger adults, particularly those between 18 and 28 years of age, were more prone to problematic online behaviors; © internet and social media addictions were positively associated with depression, anxiety, and stress and negatively associated with self-esteem; and (d) stress was found to be a significant predictor of both internet and social media addictions, while self-esteem acted as a protective factor against problematic use. These findings highlight the enduring mental health implications of increased digital engagement and emphasize the need for targeted interventions to promote healthy online behaviors, manage stress, and enhance self-esteem.