Abbas was chosen during a meeting of the Fatah central committee, two days after veteran leader Arafat was buried, a senior official said on Sunday.
Also, Palestinian prime minister Ahmad Quraya was named to head the Palestinian national security council. The decision was taken by the Fatah and the executive committee of the Palestinian Liberation Organisation (PLO) at a meeting in Ram Allah in the West Bank, a Palestinian official said.
The decision means that Quraya will have for the first time the real security powers that he sought to wrest from the veteran Palestinian leader in the months before he died on Thursday.
Meanwhile, the interim president, Rawhi Fattuh, said Palestinians would hold presidential elections on 9 January.
Arafat died on Thursday and a caretaker collective leadership now in place looks to elections to install a successor with popular legitimacy to begin reforms, combat lawlessness and revive peace talks with Israel.
Candidates will be allowed to submit their papers for the ballot for 12 days, beginning on 20 November. The campaigning period will last from 27 December until 8 January, Fattuh said.
Ahmad Quraya will, for the first
time, wield real security powers
Palestinian Cabinet Minister Saib Uraiqat said he hoped for international pressure on the Israelis to secure a free and fair vote.
"We call upon the international community to help us get the Israeli tanks and soldiers outside our populated areas in order to return the situation to that which existed," before the current round of Israeli-Palestinian fighting broke out in September 2000, he said.