The BJP will now meet on August 3 to elect the new Chief Minister of Karnataka.
"The new leader of the BJP legislature party will be elected on August 3," BJP general secretary and in-charge of party affairs in Karnataka Dharmendra Pradhan told reporters.
"Further discussions will be held over the next two days to reach consensus on the choice of the new chief minister," he said as hectic efforts by senior leaders Rajnath Singh and Arun Jaitley failed to break the impasse.
Mr Yeddyurappa and the man he wants as the next Chief Minister, Sadananda Gowda, met central BJP leaders Rajnath Singh and Arun Jaitley this evening. Sources have told NDTV that Mr Gowda is the frontrunner for the job. In fact, one of the main conditions that Mr Yeddyurappa set for stepping down was to have his candidate take over from him.
Addressing the media soon after resigning, Mr Yeddyurappa said, "As a disciplined leader of the party, I have stepped down as the Chief Minister. I served as CM for three years and two months; MLAs, MPs gave me full support during this period. I do hope and believe that my successor will also get the same support."
The new Chief Minister will take the state forward, he added.
Sadananda Gowda, a non-controversial man and a known Yeddyurappa loyalist, is not a Lingayat like Yeddyurappa, but a Vokkaliga - another dominant group in Karnataka.
Mr Yeddyurappa's exit came after he and his family were strongly indicted by Karnataka Lokayukta Justice Santosh Hegde in his report on illegal mining on Wednesday. The report kicked up a political furore with the BJP finally deciding that Yeddyurappa's continuance as Chief Minister had become untenable. (Read: Justice Hegde's report on illegal mining)
Earlier in the day, Mr Yeddyurappa's resignation was preceded by high drama when he suddenly put forward another condition - that the BJP announce the name of his successor before he demitted office. The BJP, on the other hand, wanted him to resign before announcing the name of the new Chief Minister. (Watch: Rise and fall of Yeddyurappa)
Mr Yeddyurappa had sent his resignation to party president Nitin Gadkari earlier this morning.
Later in the day, he attended his last public function as Chief Minister, where he announced his decision to quit and said he would continue working for the party.
"My dream was to make Karnataka the best state in the country. I will not rest from that aim even for a day. I am giving my resignation today. From tomorrow I will continue to work for the party," Yeddyurappa said.
"I was an ordinary party worker. I never dreamed of becoming the Chief Minister. The affection of the people put me in this chair. I worked sincerely and I am satisfied that in the last three years, the state had developed," he added.
And then, in a statement soaked in political savvy, Mr Yeddyurappa said: "It was like my arms and legs were tied. I am going to Raj Bhavan happily now without any pain in my heart. From tomorrow I can tour the state freely."