Advani, a former deputy prime minister, told party members on Sunday at a convention in the southern city of Chennai: "I have decided ... that after the Mumbai Session, I shall demit office and the party's stewardship should be taken over by other colleague," he said.
Party vice-president Mukhtar Abbas Naqvi told reporters that Advani was not resigning under pressure and it was a "voluntary" decision.
Advani brought the party to national attention by campaigning to have a Hindu temple built on the site of a 16th century Babri Mosque in the northern town of Ayodhya.
Zealots demolished the mosque in 1992, triggering Hindu-Muslim riots across the country in which more than 2000 people were killed.
The BJP won power in India in 1998 at the head of a coalition and ruled the country until May 2004, with Advani serving first as home minister and then adding the post of deputy prime minister.
Zealots demolished the Ayodhya
mosque in 1992, triggering riots
Advani took over as BJP president after its disastrous defeat in national elections in May last year. But his term was marked by controversy and frequent challenges to his authority.
Tensions peaked when Advani angered party colleagues and the BJP's ideological mentor, the Hindu right-wing party Rashtriya Swayamsewak Sangh (RSS), by describing Pakistan's founding father Mohammed Ali Jinnah as "a great man" during a visit to India's neighbour in May-June.
Advani's comments had raised the hackles of Hindu hardliners who hold Jinnah mainly responsible for the partition of the subcontinent into India and Pakistan at the end of British colonial rule in 1947.
In a thinly-veiled message on Sunday, Advani asked RSS to keep its distance with the BJP.
"Lately, an impression has gained ground that no political or organisational decision can be taken without the consent of the RSS functionaries," he said. This perception "will do no good either to the party or to the RSS".
"The BJP has to function in a manner that enables it to keep its basic ideological stance intact and at the same time expand to reach large sections of the people outside the layers of all ideology," he said.