We use polygenic risk scores (PRSs) for schizophrenia (SCZ) and bipolar disorder (BPD) to predict smoking, and addiction to nicotine, alcohol or drugs in individuals not diagnosed with psychotic disorders. Using PRSs for 144 609 subjects, including 10 036 individuals admitted for in‐patient addiction treatment and 35 754 smokers, we find that diagnoses of various substance use disorders and smoking associate strongly with PRSs for SCZ (P = 5.3 × 10−50–1.4 × 10−6) and BPD (P = 1.7 × 10−9–1.9 × 10−3), showing shared genetic etiology between psychosis and addiction. Using standardized scores for SCZ and BPD scaled to a unit increase doubling the risk of the corresponding disorder, the odds ratios for alcohol and substance use disorders range from 1.19 to 1.31 for the SCZ‐PRS, and from 1.07 to 1.29 for the BPD‐PRS. Furthermore, we show that as regular smoking becomes more stigmatized and less prevalent, these biological risk factors gain importance as determinants of the behavior.