Thousands of followers of the Indian guru, Maharishi Mahesh Yogi, have attended his cremation in the northern Indian city of Allahabad.
The Maharishi, thought to have been 91 years old, died in his sleep last week in his home in the Netherlands.
He took his Transcendental Meditation (TM) technique to the West in 1959, gaining world fame when he introduced it to the Beatles in 1968.
The technique involves the repetition of a Sanskrit mantra.
The TM movement developed into a multi-million dollar empire.
The Maharishi's followers paid tribute to him over the weekend, filing past his body which was placed in traditional cross-legged meditation posture, draped in white.
The body was cremated on a pyre by the confluence of the Ganges and Yamuna rivers, a site revered by Hindus.
Correspondents say some 2,000 followers from other parts of the world joined the crowds.
Among them was the filmmaker David Lynch.
"In life, he revolutionised the lives of millions of people," Lynch told the Reuters news agency.
"In his passing away he is bringing the West and East together as well."
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.
The Maharishi died peacefully in his sleep due to "natural causes - his age", his spokesman said.
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.
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.
Actress Mia Farrow went to study with the Maharishi
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.