"I am leaving," al-Zaatari said in a letter addressed to UN officials. "I regret to inform you that the Sudanese government asked me today to leave the country."
He added that he would depart on January 2.
Sudanese authorities, for their part, have yet to comment on the move.
The decision comes only one day after Sudan gave UNDP Sudan Director Yvonne Helle 72 hours to pack up and leave.
In the first week of December, the Sudanese government had accused al-Zaatari of "insulting Sudan and President Omar al-Bashir" in statements he allegedly made to a Norwegian newspaper.
The newspaper had quoted al-Zaatari as saying that Sudan was "in humanitarian and economic crisis" and that Sudanese society had become "totally dependent on humanitarian aid."
Al-Zaatari also reportedly told the newspaper that the international community was "compelled to deal with Sudanese President Omar al-Bashir, who is wanted by the International Criminal Court."
The UN official, for his part, said the newspaper had taken his statements out of context.
The Sudanese government announced last month that it had a plan to replace foreign humanitarian workers with Sudanese personnel.
It said the plan would go into effect next year once a partnership agreement was hammered out with the UN.
Around 21 UN-affiliated humanitarian agencies are currently operating in Sudan, along with 104 other foreign organizations.
Most of these agencies focus their activities on conflict areas, especially Sudan's western Darfur region.