Knowledge of the responses of winter wheat yield to meteorological dryness/wetness variations is crucial for reducing yield losses in Henan province, China’s largest winter wheat production region, under the background of climate change. Data on climate, yield and atmospheric circulation indices were collected from 1987 to 2017, and monthly self-calibrating Palmer drought severity index (sc-PDSI) values were calculated during the winter wheat growing season. The main results were as follows: (1) Henan could be partitioned into four sub-regions, namely, western, central-western, central-northern and eastern regions, based on the evolution characteristics of the time series of winter wheat yield in 17 cities during the period of 1988–2017. Among them, winter wheat yield was high and stable in the central-northern and eastern regions, with a remarkable increasing trend (p < 0.05). (2) The sc-PDSI in February had significantly positive impacts on climate-driven winter wheat yield in the western and central-western regions (p < 0.05), while the sc-PDSI in December and the sc-PDSI in May had significantly negative impacts on climate-driven winter wheat yield in the central-northern and eastern regions, respectively (p < 0.05). (3) There were time-lag relationships between the sc-PDSI for a specific month and the atmospheric circulation indices in the four sub-regions. Furthermore, we constructed multifactorial models based on selected atmospheric circulation indices, and they had the ability to simulate the sc-PDSI for a specific month in the four sub-regions. These findings will provide scientific references for meteorological dryness/wetness monitoring and risk assessments of winter wheat production.