From 1974 to 1981 Rajan attended Delhi Public School, R. K. Puram, In 1981 he enrolled at Indian Institute of Technology Delhi for a bachelor's degree in electrical engineering. In the final year of his four-year degree, he headed the Student Affairs Council. He graduated in 1985 and was awarded the Director's Gold Medal as the best all-round student. In 1987, he earned a Master of Business Administration from the Indian Institute of Management Ahmedabad, graduating with a gold medal for academic performance. He joined the Tata Administrative Services as a management trainee, but left after a few months to join the doctoral program at the Sloan School of Management at Massachusetts Institute of Technology.