Dyshomeostasis of copper and zinc is linked to neurodegeneration. This study investigated the relationship between circulating copper and zinc and copper/zinc ratios and cognitive function, symptoms of depression and anxiety, and neurotrophic factors in older Australian adults. In this cross-sectional study (n = 139), plasma copper, serum zinc, and neurotrophic factors (brain-derived neurotrophic factor (BDNF), vascular endothelial growth factor, and insulin-like growth factor-1) were assessed. Cognition was assessed using the Cogstate battery and the Behavior Rating Inventory (BRI) of Executive Function (Adult version). Symptoms of anxiety and depression were assessed with the Hospital Anxiety and Depression Scale. Copper (β = -0.024; 95% CI = -0.044, -0.004; p = 0.019) and copper/zinc ratio (β = -1.99; 95% CI = -3.41, -0.57; p = 0.006) were associated with lower depressive symptoms, but not cognition. Plasma copper had a modest positive association with BDNF (β = -0.004; 95% CI = 0.000, 0.007; p = 0.021). Zinc was not associated with any of the outcomes. In conclusion, greater circulating copper concentrations and higher copper/zinc ratios were associated with lower depressive symptoms (but not cognition), with copper also positively associated with BDNF concentration, in a sample of community-dwelling older adults.