The Saudi troops will conduct joint training exercises on the island alongside UAE and Yemeni forces, coalition spokesman Turki Al Malki said.
Saudi air defenses intercepted on Tuesday a ballistic missile fired by the Iranian-backed Houthi militias in Yemen towards the southern city of Jizan.
Later the same day, Houthi officials - speaking on Yemen's Al-Masirah television channel - appeared to confirm the missile launch, which they said had been aimed at "military targets" inside Saudi territory.
Maliki confirmed that the Yemeni forces have made significant progress in Saada with the support of the coalition forces, and that the Houthi missile depots were targeted in caves within Saada.
At a press briefing Monday night, he tallied six missiles in one week.
Turki al-Malki, a spokesman for a Saudi-led coalition cobbled together in 2015 to fight the Houthis, condemned the attack, which he said had targeted a civilian area "in clear violation of global law".
Riyadh accuses its regional rival Tehran of supplying the Huthis with ballistic missiles, a charge Iran denies.
"The crisis on the island is over", bin Daghr wrote on Facebook, adding that the crisis had "almost divided" the Saudi-led Arab coalition fighting Yemen's Houthi rebels.
Socotra had been spared involvement in the Yemeni conflict, which has claimed almost 10,000 lives since March 2015 and triggered what the United Nations has called the world's worst humanitarian crisis.