In the context of recent energy transition from hydrocarbon molecules to electrons, this research aims to examine the degree of substitution between renewable energy sources and fossil fuels through a dynamic framework of time‐varying parameters under state‐space model. For this purpose, this research selects four major oil‐importing countries and employs annual time series data for crude oil imports, gross domestic product, crude oil price, renewable energy consumption, population growth, real effective exchange rate and industrial production index for each country in the sample while covering the period 1991–2018. The estimates reveal positive and significant income, population and industrial production index elasticities for most of the countries in the sample. In addition, this research finds negative and statistically significant elasticity between renewable energy consumption and demand for imported crude oil for India, China and Japan, although magnitude is very small. However, there is insignificant and little substitution for US data. This research is unique as to our knowledge there is no such study available before and it provides insights for policymakers in oil‐exporting countries to develop sustainable long‐term diversification strategies to reduce reliance on oil revenues.