Drought is a major factor affecting the sustainable development of society and the economy. Research on drought assessment is of great significance for formulating drought emergency policies and drought risk early warning and enhancing the ability to withstand drought risks. Taking the Yellow River Basin as the object, this paper utilizes data fusion, copula function, entropy theory, and deep learning, fuses the features of meteorological drought and hydrological drought into a drought assessment index, and establishes a long short-term memory (LSTM) network for drought assessment, based on deep learning theory. The results show that (1) after extracting the features of meteorological drought and hydrological drought, the drought convergence index (DCI) built on the fused features by copula function can accurately reflect the start and duration of the drought; (2) the drought assessment indices were effectively screened by judging the causality of the drought system, using the transfer entropy; (3) drawing on the idea of deep learning, LSTM for drought assessment, which was established on DCI and the drought assessment factors, can accurately assess the drought risks of the Yellow River Basin.