Drought is a complicated hydrometeorological disaster and could cause severe impacts on agriculture. The precipitation or soil moisture based drought index is capable of monitoring a specific drought type and may fail to capture the overall drought development and may underestimate the integrated drought impact. Here a parametric multivariate drought index SPESMI is developed by combining precipitation, potential evapotranspiration (PET) and root-zone soil moisture variables using a series of univariate distribution functions and copulas. Specifically, the PET is calculated based on the modified Hargreaves equation and the minus of precipitation and PET (PPET) is used to represent meteorological drought. PPET and soil moisture are modeled using multiple distributions separately to calculate the Standardized Precipitation Evapotranspiration Index (SPEI) and the Standardized Soil Moisture Index (SSMI), respectively. Then PPET and soil moisture are jointly modeled based on four parametric copulas and the optimal copula is selected based on the Kolmogorov–Smirnov statistic with maximum p-value. The parametric index SPESMI has advantages over nonparametric approaches as the former is more suitable for the modeling of tails and extreme events than the latter. The SPESMI index exhibits an overall better correlation with wheat yield for most of the cities within Henan province, China, than SPEI, SSMI, soil moisture drought index (SODI) and vegetation-soil water deficit (VSWD) index. The drought conditions under climate change are projected using various drought indices and SPEI and SSMI show divergent drought trends. The SPESMI integrates the drought information from meteorological and hydrological conditions and suggests more severe and frequent droughts under climate change relative to historical periods. The developed parametric multivariate drought index SPESMI is useful for integrated regional drought monitoring and agricultural impact assessment versus two univariate and two multivariate drought indicators.