The redeployment was agreed under the ceasefire 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 starvation.
The UN says the Huthi rebels announced late on May 10 that they would unilaterally redeploy their forces out of three Red Sea port facilities over four days beginning on May 11 - potentially opening the way for the delivery of humanitarian aid needed to prevent a starvation that threatens millions of people.
Yemen's Houthi rebels will begin a pullback from ports in the flashpoint city of Hodeida on Saturday, the first practical step on the ground since a ceasefire deal was reached in December, the head of a United Nations redeployment committee has said.
The Houthi representative in a joint coordination team, Brigadier Mohammed al-Qaderi said via Twitter: "We have implemented all obligations of the first phase of redeployment".
The UN's Redeployment Coordination Committee (RCC), led by Danish Lieutenant General Michael Lollesgaard, head of the UN observer team in Hodeida, drew up the redeployment plans under a pact agreed last December in Stockholm, Sweden, the first major breakthrough in peace efforts to end a war that has killed tens of thousands and pushed Yemen to the brink of starvation.
The Houthi-run Al Masirah TV channel said United Nations observers were monitoring the troop redeployment which is expected to take four days in total.
The governor of Hodeidah, al-Hassan al-Taher, stated that the move did not comply with the agreed upon terms of the Stockholm Agreement.
The UN mission will monitor the redeployment, a first step towards concluding the peace agreement, the UN statement said, adding that it must be followed by "the committed, transparent and sustained actions of the parties to fully deliver on their obligations".
But they've yet to announce a withdrawal.
The move, which has yet to be verified by the United Nations and accepted by the Saudi-led coalition, is the first major step in implementing a deal reached by the Saudi-backed government and the Iran-aligned Houthis for a ceasefire and troop withdrawal in Hodeidah last year, part of worldwide efforts to end the four-year conflict.
The port of Hodeida is one of Yemen's most important lifelines.
Humanitarian officials have long pleaded with Yemen's warring sides to spare Hodeida, a lifeline for the crippled economy, dependent on the World Food Programme's biggest aid operation to feed more than 10 million people.
The peace deal had stalled since January amid deep mistrust among the warring parties in a conflict that has killed tens of thousands and pushed the Arabian peninsula nation to the brink of starvation.
A Sunni-Muslim coalition led by Saudi Arabia intervened in Yemen in March 2015, to push back against an advance by the rebels and restore power to President Abed Rabbo Mansour Hadi.