The Chouli Mutt pontiffs sat on the pyre made by them using the firewood stored to prepare food for mass feeding and set fire to it near the sanctum sanctorum where they slept regularly, they said.
The three were identified as Jagannatha Swamy (around 30), Pranava Swamy (17) and Era Reddy (about 40), Deputy Superintendent of Police V M Jyothi told PTI.
The extreme step by the pontiffs, whose bodies were charred beyond recognition, came six weeks after their senior Ganesh Avadhoota Swamy died mysteriously, which is being probed by police.
"The government will take necessary steps to investigate the matter and find out the truth," he said in a statement.
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A suicide note found near the pyre said, "We have no enemies. We will go where our senior seer has gone...God is everything for us. Please do not disturb or harass anyone", according to police.
The Mutt was established 25 years ago by Ganesh Avadhoota, one of whose disciples had disappeared in January and his whereabouts are not known.