Hamas announced on Sunday the nomination in a text message, a day after its members were sworn into the new Hamas-dominated Palestinian parliament.
The nomination was widely expected. Haniya, 46, is seen as a leader of the more pragmatic wing of Hamas.
Palestinian leader Mahmoud Abbas was expected later on Sunday to formally charge Haniya with the task of putting together a new cabinet. Haniya would then have three weeks to submit a government to Abbas for approval.
Addressing the parliament on Saturday, Abbas said he expected Hamas to honour existing peace accords with Israel and halt violence. Hamas leaders rejected those calls, but signalled a willingness to compromise.
Israel's acting prime minister, Ehud Olmert, ruled out any contacts with a Hamas-led government. The group has killed hundreds of Israelis in bombings and does not recognise Israel.
Born in Gaza's Shati refugee camp, Haniya graduated from Gaza City's Islamic University in 1987 with a degree in Arabic literature, and became a close associate of Hamas founder Shaikh Ahmad Yasin.
Haniya rose in importance after
Shaikh Ahmad Yasin was killed
Haniya was expelled by Israel to south Lebanon in 1992, returned to Gaza a year later and became the dean of the Islamic University.
In 1998, he took charge of Yasin's office.
A pragmatist, he served as a liaison between Hamas and the Palestinian Authority, established in 1994 and dominated by the rival Fatah movement.
He rose to prominence after Israel's assassinations in 2004 of Yasin and Yasin's successor, Abd al-Aziz al-Rantisi.
He has been a member of the political leadership of Hamas since the 1990s.