The Maharishi built up a following of about six million people
The Maharishi, thought to have been 91 years old, died in his sleep on Tuesday evening at his home in the Netherlands.
He introduced the Transcendental Meditation movement to the West in 1959, with the intention of creating individual peace and enlightenment.
By the time of his death, it had grown into a multi-million dollar empire.
The Maharishi announced his retirement and retreat into silence at his home in Vlodrop last month, saying his work was done and that he wanted to dedicate his remaining days to studying ancient Hindu Vedas texts.
"He had been saying he had done what he set out to do," his spokesman, Bob Roth, told the Associated Press.
Mr Roth said the Maharishi died peacefully in his sleep at around 1900 (1800 GMT), due to "natural causes - his age".
Born in the Indian state of Madhya Pradesh, the Maharishi trained as a physicist before devoting himself to spiritual enlightenment.
After studying in the Himalayas under Guru Dev during the 1940s and 1950s, he spread the teachings of transcendental meditation throughout the world.
Based on the theory and practice of yoga, transcendental meditation involves a mental technique that can reportedly be easily learnt and practised by anyone to reach a "state of pure consciousness" and gain deep rest.
By repeating in the mind a Sanskrit mantra, a short word or phrase, a practitioner is supposedly able to find deep relaxation, which in turn leads to enhanced inner joy, vitality, and creativity.
"Don't fight darkness. Bring the light, and darkness will disappear," the Maharishi said in an interview in 2006, repeating one of his own mantras.
The Maharishi introduced the technique to the US in 1959, but it did not become widely known in the West until 1968, when the Beatles travelled to India to meditate with him, although the band famously later fell out with him.
Despite this, transcendental meditation's 20-minute routine came to be widely used in the worlds of education, business and welfare to reduce stress and improve concentration, eventually building a following of five million people.
Donations and the $2,500 (£1,270) fee to learn the technique helped finance the construction of Peace Palaces, or meditation centres, in dozens of cities around the world, as well as several universities.
After decades of teaching, the Maharishi unveiled plans to use the power of group meditation to create world peace and end poverty.In 1990, he moved into 200-room mansion in the southern Dutch village of Vlodrop. Concerned about his fragile health, he secluded himself in two rooms, speaking only by video link even to his closest advisers in the same building.