We aimed to compare the relationship between hypertension and obesity-related anthropometric indices (waist circumference [WC], waist-height ratio, waist-hip ratio [WHR], and body mass index; unconventional: new body shape index [ABSI] and body roundness index [BRI]) to identify best predictors of new-onset hypertension. The study included 4123 adult participants (2377 women). Hazard ratios (HRs) and 95% confidence intervals (CIs) were determined using a Cox regression model to estimate the risk of new-onset hypertension with respect to each obesity index. In addition, we assessed the predictive value of each obesity index for new-onset hypertension using area under the receiver operating characteristic curve (AUC) after adjusting for common risk factors. During the median follow-up of 2.59 years, 818 (19.8%) new hypertension cases were diagnosed. The non-traditional obesity indices BRI and ABSI had predictive value for new-onset hypertension; however, they were not better than the traditional indexes. WHR was the best predictor of new-onset hypertension in women aged ≤ 60 and > 60 years, with HRs of 2.38 and 2.51 and AUCs of 0.793 and 0.716. However, WHR (HR 2.28, AUC = 0.759) and WC (HR 3.24, AUC = 0.788) were the best indexes for predicting new-onset hypertension in men aged ≤ 60 and > 60 years, respectively.