Twenty-three people had put their names forward for the vote, which follows years of war.
Interim President Hamid Karzai is the favourite to win, but he faces strong challenges from three main contenders.
Uzbek general Abdul Rashid Dostum, ex-education minister Yunus Qanuni and Hazara leader Mohammed Mohaqiq all made it through the vetting process.
Mr Qanuni, a leader in the Northern Alliance, has the backing of the powerful Defence Minister Mohammed Qasim Fahim and the Foreign Minister Abdullah Abdullah.
General Dostum is expected to win the support of the Uzbek and Turkmen ethnic minorities in the north.
Mr Mohaqiq has a very loyal following among the Shia Hazaras of central Afghanistan and is also likely to get many votes from Hazaras still living as refugees in Iran and Pakistan.