Solar Irradiance depicts the light energy produced by the Sun that hits the Earth. This energy is important for renewable energy generation and is intrinsically fluctuating. Forecasting solar irradiance is crucial for efficient solar energy generation and management. Work in the literature focused on the short-term prediction of solar irradiance, using meteorological data to forecast the irradiance for the next hours, days, or weeks. Facing climate change and the continuous increase of greenhouse gas emissions, particularly from the use of fossil fuels, the reliance on renewable energy sources, such as solar energy, is expanding. Consequently, governments and practitioners are calling for efficient long-term energy generation plans, which could enable 100% renewable-based electricity systems to match energy demand. In this paper, we aim to perform the long-term prediction of solar irradiance, by leveraging the downscaled climate simulations of Global Circulation Models (GCMs). We propose a novel Bayesian deep learning framework, named DeepSI (denoting Deep Solar Irradiance), that employs bidirectional long short-term memory autoencoders, prefixed to a transformer, with an uncertainty quantification component based on the Monte-Carlo dropout sampling technique. We use DeepSI to predict daily solar irradiance for three different locations within the United States. These locations include the Solar Star power station in California, Medford in New Jersey, and Farmers Branch in Texas. Experimental results showcase the suitability of DeepSI for predicting daily solar irradiance from the simulated climate data. We further use DeepSI with future climate simulations to produce long-term projections of daily solar irradiance, up to year 2099.