Background Depression and anxiety are common psychiatric complications affecting patients with diabetes mellitus. However, data on the prevalence of depression, anxiety, and associated factors among Malaysian diabetic patients is scarce. The Anxiety, Depression, and Personality Traits in Diabetes Mellitus (ADAPT-DM) study aimed to determine the prevalence of depression and anxiety, and their associated factors in the Malaysian diabetic population. Methods This cross-sectional study recruited 300 diabetic patients via convenience sampling from the Endocrine outpatient clinic of Universiti Kebangsaan Malaysia Medical Centre, a tertiary referral healthcare facility in Kuala Lumpur. Socio-demographic characteristics and clinical history were obtained from each participant. The Generalised Anxiety Disorder-7 (GAD-7) was administered to assess anxiety symptoms, the Beck Depression Inventory (BDI) to assess depressive symptoms, the Big Five Inventory (BFI) to evaluate personality traits, and the World Health Organization Quality of Life-BREF (WHOQOL-BREF) to measure quality of life (QOL). Multivariate logistic regression analyses were performed to determine the association between various factors, and depression and anxiety. Results The prevalence of depression was 20% (n = 60) while anxiety was 9% (n = 27). Co-morbid depression (adjusted OR = 24.91, 95% CI = 5.67–109.42, p < 0.001), neuroticism (adjusted OR = 9.24, 95% CI = 2.03–42.03, p = 0.004), and greater physical health-related QOL (adjusted OR = 1.67, 95% CI = 1.07–2.59, p = 0.024) increased the odds of developing anxiety, while psychological QOL (adjusted OR = 0.41, 95% CI = 0.21–0.79, p = 0.008) was protective. Co-morbid anxiety (adjusted OR = 20.06, 95% CI = 4.70–85.57, p < 0.001) increased the odds of depression, while older age (adjusted OR = 0.96, 95% CI = 0.92–0.99, p = 0.012), regular religious practice (adjusted OR= 0.08, 95% CI= 0.01-0.56, p= 0.011) and physical health-related QOL (adjusted OR = 0.72, 95% CI = 0.59–0.89, p = 0.002) were protective. Conclusions The study findings signify the need to screen for co-morbid depression and anxiety, as well as personality traits and QOL, and to include psychosocial interventions when planning a multidisciplinary approach to managing diabetes.