Mr Chaleo rose from humble origins to become one of Thailand's richest men, with a wealth estimated at $5bn (Â£3.2bn) last year.
His pharmaceutical company produced a tonic drink in the 1970s, but it became popular worldwide in the next decade when he went into partnership with an Austrian entrepreneur.
Red Bull also owns two football clubs and a Formula 1 team.
Mr Chaleo was born of poor Chinese immigrant parents in the northern province of Phichit, reportedly in 1932, local media say.
He worked as a salesman before setting up TC Pharmaceuticals in 1962.
It introduced the drink Krating Daeng, which became popular with shift workers and lorry drivers.
In 1984 he launched it as Red Bull with the Austrian marketing expert Dietrich Mateschitz, and three years later began selling it in Austria.
Red Bull is now sold in 70 countries throughout the world.
Forbes Magazineput him equal 205th in its March 2012 world billionaire list.
The creator of the energy drink Red Bull, Chaleo Yoovidhya, has died.