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Power grid operators rely on solar irradiance forecasts to manage uncertainty and variability associated with solar power. Meteorological factors such as cloud cover, wind direction, and wind speed affect irradiance and are associated with a high degree of variability and uncertainty. Statistical models fail to accurately capture the dependence between these factors and irradiance. In this paper, we introduce the idea of applying multivariate Gated Recurrent Units (GRU) to forecast Direct Normal Irradiance (DNI) hourly. The proposed GRU-based forecasting method is evaluated against traditional Long Short-Term Memory (LSTM) using historical irradiance data (i.e., weather variables that include cloud cover, wind direction, and wind speed) to forecast irradiance forecasting over intra-hour and inter-hour intervals. Our evaluation on one of the sites from Measurement and Instrumentation Data Center indicate that both GRU and LSTM improved DNI forecasting performance when evaluated under different conditions. Moreover, including wind direction and wind speed can have substantial improvement in the accuracy of DNI forecasts. Besides, the forecasting model can accurately forecast irradiance values over multiple forecasting horizons.