Handgrip strength (HGS) is strongly associated with hypertension (HTN), diabetes mellitus (DM), and HTN and DM comorbidity (HDC). However, no studies have simultaneously examined anthropometric and absolute/relative HGS indices among HTN, DM, and HDC patients. The objective of this study was to examine the associations of anthropometric and HGS indices with HTN, DM, and HDC. For this large-scale cross-sectional study, we used a dataset from the Korea National Health and Nutrition Examination Survey. The study population included 15,343 participants aged 50 years and older. Complex sample binary logistic regression was used to examine the associations of each disease with the anthropometric and HGS indices in crude and adjusted models. The prevalence of HTN, DM, and HDC in the study population was 35.1%, 8.6%, and 14.4% in men and 34.7%, 5%, and 11.8% in women, respectively. In men, the indices with the strongest associations with HTN, DM, and HDC were body mass index, waist circumference, and waist-to-height ratio. Among women, body mass index and waist-to-height ratio had the strongest associations with HTN. Waist circumference and waist-to-height ratio had the strongest associations with DM. Waist-to-height ratio had the strongest associations with HDC. Additionally, the relative HGS indices were more strongly associated with these diseases than the absolute HGS indices. HGS indices were associated with HTN, DM, and HDC, but compared with the absolute HGS index and relative HGS indices, anthropometric indices were more strongly associated with these diseases in the Korean population.