The tapes have BJP leaders including the Chief Minister allegedly trying to persuade Congress lawmaker BC Patil to switch sides.
One of the tapes has the voice of Mr Yeddyurappa, the Congress alleged. The other tape, said the party, has his son Vijayendra.
In one of the tapes, the Congress claimed, Mr Yeddyurappa can be heard asking lawmaker BC Patil to get off the bus taking Congress lawmakers out of Karnataka and support the BJP. The Congress alleges that Mr Yeddyurappa is heard offering him the position of a minister.
"Don't go to Kochi, come back. Come back, we'll make you a minister and help you in whatever way you want," the person who the Congress claims is Mr Yeddyurappa, can be heard saying.
NDTV cannot independently verify the authenticity of the audio tapes.
"Janardhan Reddy clearly says he has the backing of BJP president Amit Shah for doing horse-trading (sic)," the Congress alleged in a tweet after its leaders played out the clip at a media briefing.
Union Minister Prakash Javadekar rubbished the Congress charge. "There is a reference to Amit Shah in it... Amit Shah doesn't do this... Several such lies have been exposed," the senior BJP leader, calling the tape "false propaganda".
According to the clip released by the Congress, a man, who was introduced as Janardhan Reddy, promises Congress lawmaker Basangouda Daddal of a ministerial berth and more for his support.
The Congress and Janata Dal Secular, which made a joint bid for power after the BJP emerged as the single largest party in last week's Karnataka assembly elections, has been struggling to keep its flock together after Governor Vajubhai Vala invited Mr Yeddyurappa to form the government.
The Congress-JDS combine had initially sequestered the lawmakers in Bengaluru hotel but packed them off to Telangana capital Hyderabad about 600 km away to insulate them from pressures from the BJP. Later the Congress also asked its legislators to install a phone recording app so that they can record offers made by the BJP to them.