Hickey stepped aside after being arrested by Rio police during the 2016 Olympics in an investigation into illegal ticket sales.
Acting president Willie O'Brien, Swim Ireland's chief executive Sarah Keane and Basketball Ireland's Bernard O'Byrne are the three candidates.
Hickey, 71, was allowed to return home to Ireland in December.
This was after the the umbrella group for Olympic Committees throughout the world agreed to pay his bail of just under £330,000.
The Dubliner, who was also president of the European Olympic committees before his arrest in Brazil last August, has said he is "totally innocent" of the charges levelled at him by the Brazilian police.
O'Brien, 68, has served in various roles with the OCI for more than 20 years, including the last 12 years as vice-president.
After Hickey stepped down from the role, O'Brien became the organisation's acting president.
O'Brien, a close associate of Hickey's, is regarded as the continuity candidate, while Keane, 43, has served on the OCI's council for two years with former Football Association of Ireland chief executive O'Byrne, 62, portraying himself as the change candidate.
The OCI's 34 member federations and members of the governing body's council will choose Hickey's successor.
Earlier this week, Hickey released a statement saying he would have "no role" in Thursday's vote and that he would not be able to attend the gathering following a recent medical procedure on his heart.
"Accordingly, the time has now come to pass the Irish Olympic torch to a new generation and I wish nothing but the best of luck and success to the new president, officers and executive committee of the OCI," Hickey added.
Thursday's vote is taking place at an OCI extraordinary general meeting in Dublin's Conrad Hotel.
The Olympic Council of Ireland (OCI) will elect a new president to succeed Pat Hickey on Thursday night in Dublin.