Abbas, who has already replaced Arafat as chairman of the Palestine Liberation Organisation (PLO), was named by the Fatah central committee as the party's candidate three days ago.
His nomination needed final approval from the group's Revolutionary Council, which was given during a meeting late on Thursday in the West Bank city of Ram Allah.
Of the 99 council members present, 97 voted for Abbas and two abstained, Palestinian cabinet secretary Tayib Abd al-Rahim said.
Many of those who failed to attend from the 129-member strong body were from Gaza and were unable to travel to the West Bank because of Israeli travel restrictions, he added.
It emerged earlier on Thursday that jailed West Bank Fatah leader Marwan al-Barghuthi also intends to run for in the 9 January presidential race.
Members of Fatah's higher committee, which is still officially headed by al-Barghuthi, said the 45-year-old had sent a message via his lawyer that he wanted to succeed Arafat.
But with Abbas confirmed as Fatah's candidate, al-Barghuthi would have to run as an independent.
Ahmad Ghnim, of the Fatah Revolutionary Council, said its approval of Abbas' candidacy meant "the door was closed" to al-Barghuthi running on the Fatah ticket.
But it remains to be seen whether he is really prepared to divide Fatah.
Al-Barghuthi insisted on the need for Palestinians to "retain our national unity" in a message issued immediately after Arafat's death a fortnight ago.