Shbeir, who has a PhD in microbiology from the University of West Virginia in the US, was president of the Islamic University in Gaza for 15 years until 2005 and has no previous political career.
The academic is believed to have close ties to Hamas, has maintained good relations with all the Palestinian factions, and frequently met the late Yasser Arafat.
Shbeir, originally from the town of Khan Younis in Gaza, lives in Gaza City with his six children and his wife, who serves as deputy to the minister of women's affairs.
Abbas agreed to the appointment after a meeting between officials from the ruling Hamas party and Fatah in Gaza.
A presidential aide said: "Hamas proposed three names all of which were acceptable to president Abbas and Hamas indicated that their favoured choice was Mohammed Shbeir."
Months of talks have failed to lead to the establishment of a unity government, but in recent days both sides said progress had been made, and Abbas said he hoped a government would be in place by the end of November.
Civil servants held mass protests
over unpaid wages
The two sides hope that the unity government would be acceptable to the international community, which has refused to deal with the Hamas-led government until it renounces violence, recognises Israel and accepts existing peace deals.
Financial sanctions and Israel's withholding of revenue it collects on behalf of the Palestinians have made it largely impossible for the government to pay its 165,000 civil servants, leading to widespread hardship and protests in the West Bank and Gaza Strip.
Abbas is travelling to Jordan on Monday to update officials on efforts to form the unity government before heading to Cairo on a similar mission, an official said.
He is expected in to meet King Abdullah II on Tuesday to discuss "the latest developments on the Palestinian scene".
Ehud Olmert, the Israeli prime minister, said in an interview with the Palestinian newspaper al-Quds, that he was willing to talk to Hamas if it accepted the conditions laid down by the international community.
"If Hamas accepts the quartet conditions, I will sit down with them," he said.
Olmert noted that Israel once refused to deal with the Palestine Liberation Organisation, considering it a terrorist organisation, but now talks to its representatives, including Abbas, its leader.