The long-delayed withdrawal of rebel forces will be completed by Tuesday, General Michael Lollesgaard said in a statement.
The redeployment of forces was agreed under the ceasefire deal reached in Sweden that offered the best hope in years of moving toward an end to the war that has pushed Yemen to the brink of famine.
Lollesgaard said he "welcomes the offer and intention" of the Houthis "to undertake an initial unilateral redeployment from the ports of Hodeida, Saleef and Ras Issa."
UN assessing damage at Yemeni port city grain mills
A UN observer mission, also led by the Danish general, will monitor and report on the redeployment.
The United Nations announced a deal on the two-stage pullback from Hodeida city and its ports in February, but the redeployment failed to materialise on the ground as the peace effort stalled.
UN diplomats said the Houthis had refused to pull back from the ports as part of the first stage, citing fears that forces linked to the Saudi-led coalition would move in to take over those facilities.
Hodeida is the main entry point for the bulk of Yemen's imports and humanitarian aid, providing a lifeline to millions on the brink of famine.
The Saudi-led coalition intervened in Yemen in March 2015 to push back an advance by the rebels, who continue to hold the capital Sanaa, and to restore to power President Abedrabbo Mansour Hadi.
The conflict has killed tens of thousands people, many of them civilians, relief agencies say.
The fighting has triggered what the United Nations describes as the world's worst humanitarian crisis, with 24.1 million -- more than two-thirds of the population -- in need of aid.
Since the Stockholm agreement, the United Nations has struggled to turn details of that deal into reality on the ground, and several deadlines have been missed.
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