Doctors say the 84-year-old guru, who is thought to have millions of followers around the world, died following a cardiac arrest.
He had been admitted to hospital in his hometown of Puttaparthi last month, suffering from respiratory problems and kidney failure.
His followers include former Indian prime ministers and Bollywood stars.
Many of his supporters consider him a living god and credit him with mystical powers including the ability to conjure objects out of thin air.
But his career had also been dogged by controversy. He had been accused of faking some of the so-called miracles attributed to him.
And some former followers have levelled accusations of sexual abuse against him and other members of his ashram - allegations that he has denied.
He has never been charged by police in connection with these allegations.
Officials say his body will be kept for public viewing for the next few days and a funeral is expected to take place after that.
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