Advani, who was asked by the RSS to resign in the wake of his controversial remarks on Mohammad Ali Jinnah, made the announcement in his concluding remarks to the National Executive in Chennai, party sources said.
He also attacked the Sangh leadership that the perception that it was controlling the Saffron party was neither good for either the party or the Sangh itself, sources said.
Later, party Vice-President Mukhtar Abbas Naqvi told reporters that Advani was not resigning under pressure and it was a "voluntary" decision.
The Mumbai Plenary to mark the conclusion of the party's silver Jubilee celebrations will be held in Mumbai on December 28 and 29. Naqvi said a new party President would be nominated by then.
Maintaining that he had accepted the responsibility as party president in October 2004 as his predecessor Venkaiah Naidu had some personal problems, Advani said, "I have decided however that I shall demit office and the party stewardship should be taken over by some other colleague."
He said the BJP leadership has had no hesitation in consulting RSS functionaries "from time to time depending on the issue at hand."
"After such consultations, the party takes its own independent decisions. Some of these decisions may differ, and have indeed differed, from the stated positions of the RSS and certain constituents of the Sangh Parivar," senior Party leader Jaswant Singh told reporters in Chennai quoting from Advani's concluding statement.
The BJP chief, however, regretted "that lately an impression has gained ground that no political or organisational decision can be taken without the consent of the RSS functionaries.
"This perception, we hold, will do no good either to the party or to the RSS. The RSS too must be concerned that such a perception will dwarf its greater mission of man-making and nation-building. Both the RSS and the BJP must consciously exert to dispel this impression," Advani said.
Nonetheless, he said the RSS should continue to play its role to strengthen the ethical, moral and idealistic moorings of the workers as well as functionaries of BJP as in the past and "this is in the larger interest of the nation."
The BJP, Advani said, greatly appreciated the continuing interaction with RSS and other sister organisations. "Their views provide valuable inputs for our decision making process, But the BJP as a political party is accountable to the people, its performance being periodically put to test in elections.
"So in a democratic multi-party polity, an ideologically driven party like the BJP has to function in a manner that enables it to keep its basic ideological stances intact and at the same time expand itself to reach the large sections of the people outside the layers of all ideology," he said.
Earlier, in his valedictory address, former Prime Minister Atal Bihari Vajpayee heaped lavish praise on Advani saying he had always worked indefatiguably in the background and never asserted himself in the forefront.
Vajpayee recalled, "the great help, contribution and assistance" he received from Advani since his first term in Parliament. The former prime minister also stressed on the "Need for exercising freedom of expression with due sense of discipline and restraint."
Asked whether Advani was quitting under pressure from RSS, Jaswant Singh said, "I don't think he is a person who succumbs and his statement also does not indicate that."
To a question on who would succeed Advani, Jaswant Singh said, "I hold no office and it is the function of the party organisation to choose his successor."
Asked if he was a possible choice, the former external affairs minister said, "I have no such desire."
On whether he agreed with Advani's observations on RSS, Singh said, "I am a disciplined soldier of the party and will never disagree with the President and certainly not in front of the press."
Asked about the party's reaction on Advani's decision to step down, he said "the party backs him in all his decisions and BJP looks to the future with confidence. We have a mission to fulfill."
Singh replied in the negative when asked if Advani had been a stopgap arrangement and said his ascension was a "collective decision" of the party.
He also categorically asserted that Advani's decision would not have any adverse impact on the party's performance in the Bihar Assembly elections next month. "We feel we will continue to achieve what we have set for ourselves that is to unseat the unholy and corrupt organisation of the RJD-Congress combine."