Abbas is under pressure at home and abroad to clean up the corrupt structures bequeathed by Arafat, who died on 11 November after decades as leader of the Palestinian fight for a state.
Officials said Abbas had fired 50 of 55 civilian and military advisers - although well over 1000 staff were still employed by Arafat's office in the West Bank city of Ram Allah.
"It's an empire," said one official. "This is an important step that will be followed by more such changes to make administrative and security reforms."
The names of those fired were not immediately available.
Reforms are seen as key to a big increase in donor funding for the Palestinian Authority as well as prospects for talks with Israel.
The style of Abbas, a former businessman, is different from that of Arafat, who had faced an upsurge of demands for internal change in the months before his death.
Abbas sticks by Arafat's key positions for a Palestinian state in the West Bank, Gaza and East Jerusalem, seized by Israel in the 1967 Middle East war and for a right of return for Palestinian refugees to homes in land Israel has occupied.
But he has called for an end to the four-year-old uprising to allow renewed talks with Israel.