"The crisis on the island is over," Bin Dagher wrote on Facebook, adding that the crisis had "almost divided" the Saudi-led Arab coalition fighting Yemen's Huthi rebels.
The announcement came a day after Saudi troops were deployed to the strategic island following tensions between Yemen's internationally recognised government and the UAE, a key member of the coalition.
Under the deal the two countries' troops will withdraw from Socotra and Yemeni forces will be stationed at the island's airport and port, the agency reported.
The presence of UAE troops angered Socotra residents, who insisted there were no rebels on the island, the source said.
Socotra had been spared involvement in the Yemeni conflict, which has claimed nearly 10,000 lives since March 2015 and triggered what the United Nations has called the world's worst humanitarian crisis.
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