Ismail Haniya, until recently head of Hamas in the Gaza Strip, said the results of internal elections will be announced "in the coming days".
A high-ranking Hamas official told AFP that the new leadership will be announced before May 15.
The official said Haniya is likely to be named the new head of the movement, replacing Khaled Meshaal who lives in Doha in exile and has completed the maximum two terms in office.
Tomorrow in Qatar, Hamas will unveil a supplementary charter that will formally accept the idea of a state in the territories occupied by Israel in the Six-Day War of 1967.
Some analysts say the move is a bid to ease Hamas's international isolation.
The original 1988 charter will not be dropped, just supplemented, and there will be no recognition of Israel, as demanded by the international community.