"The Sudanese authorities have agreed to let us resume our work in covering Sudan," Al-Musallami Al-Kabbashi said.
The Al-Jazeera crew had been informed in late May, at the height of the protests that brought down longtime ruler Omar al-Bashir, that their licence and work permits were being withdrawn.
The news channel's staff had handed over equipment and closed down the office after being notified of the decision by the country's Transitional Military Council.
Egypt, the United Arab Emirates and Saudi Arabia broke off diplomatic ties with Doha in 2017, accusing it of terrorism, which it denies.
The generals, backed by those three powers, had resisted calls from African and Western governments to hand over the reins of power until a political deal was eventually reached with protest leaders last month.
A compromise for a 39-month transition to civilian rule was sealed on August 4 and is due to be officially signed on Saturday, during a ceremony to be attended by several foreign dignitaries.
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