"The crisis on the island is over," Ahmed bin Dagher wrote on Facebook, adding that the crisis had "almost divided" the Saudi-led Arab coalition fighting Yemen's Houthi rebels.
The announcement came a day after Saudi troops were deployed to the strategic island -- which lies at the exit of a bustling shipping lane between the Mediterranean and Indian Ocean -- following tensions between Yemen's internationally recognised government and the UAE, a key member of the coalition.
Dagher's comments come after an agreement was signed on Sunday evening with the UAE and Saudi Arabia, both part of the coalition, according to the state-run Saba news agency.
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 crisis was triggered after the Yemeni government of President Abedrabbo Mansour Hadi protested the deployment of UAE troops to the island.
According to a goverment source AFP spoke to, Emirati soldiers were deployed to Socotra earlier this month without the approval of Hadi's government.
The presence of UAE troops angered Socotra residents, who insisted there were no rebels on the island, the source added.
Although the UAE has played a role in the Saudi-led coalition's fight against the Houthis, it also recently distanced itself from the Riyadh-based President Hadi.
The Emiratis have instead been expanding their influence in southern Yemen, and also back separatists who wrenched control of the south of the country from Hadi in January.
Socotra had been spared involvement in the Yemeni conflict, which has claimed nearly 10,000 lives since March 2015 and triggered what the UN has called the world's worst humanitarian crisis.
In a separate incident on Monday, Houthi rebels said they launched a ballistic missile at Saudi Aramco facilities in the southwestern Jizan province.
Saudi air defences had tracked the rocket, which landed in an uninhabitated area of the kingdom, according to the Saudi Press Agency.
Monday's missile follows a salvo of Houthi missiles that were fired at Saudi Arabia last week, one of which fell short of the capital Riyadh.
Agencies contributed to this report.
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