Barca said candidates could register between May 25 and June 1 and needed to collect at least 2,095 signatures of support to be considered.
Barcelona, along with La Liga rivals such as Real Madrid and Athletic Bilbao, are run as sports clubs with thousands of members who choose who runs their club for fixed terms in office.
The election campaign will run from June 4-11.
Laporta's second term in office finishes at the end of June and he has to stand down, having presided over one of the most successful periods for the club.
Since he arrived in 2003, Barca have won two European Cups, three league titles and a King's Cup. They have a chance to add another La Liga title to the list as they top the standings with four games left to play this season.
One of the new president's most pressing tasks will be to secure the future of coach Pep Guardiola, who helped them to win six trophies in 2009.
Guardiola has agreed with Laporta to extend his contract to next season but has refused to sign a deal until he has spoken with the incoming president.
