0426 GMT February 21, 2020
The official, who requested anonymity, said the Houthis began to pull back from the Red Sea port at midnight (2100 GMT Friday), AFP reported.
The withdrawal from the port, which is the point of entry for food aid to some 14 million Yemenis UN agencies say are on the brink of famine, is a key part of a cease-fire that went into effect on December 18.
Saudi-backed forces are also supposed to pull back from parts of the city they recaptured in an offensive they launched on June 13.
The Houthis began "the first phase of redeployment from the Hodeida port", a Houthi official told Saba news agency. The Houthis held a ceremony to mark the occasion.
The UN Security Council last week unanimously approved a resolution authorizing the deployment of observers to oversee a hard-won truce for Hodeida that was agreed by the Saudi-backed former government and the Houthis in Sweden this month.
Retired Dutch general Patrick Cammaert is heading a joint truce monitoring committee, which includes both former government and Houthi representatives, and chaired its first meeting this week.
The UN-led panel addressed "the first phase of the implementation of the agreement... based on ceasefire, confidence building measures to deliver humanitarian assistance and redeployment", a UN statement said.
It added that the panel would convene again on January 1 to discuss "detailed plans for full redeployment".
The UN also said that a humanitarian convoy was expected later Saturday to leave Hodeida port and travel along the main road that links it to the Houthi-held capital Sana’a. Its destination was not immediately clear.
"As a confidence building measure, the parties have agreed to begin opening blocked humanitarian corridors, starting with the Hodeida-Sana’a road, followed by other routes, in a phased manner," said the statement.
The truce has remained shaky, with the two sides accusing each other of violations.
A resident reached by telephone on Saturday said former government and Houthi forces had exchanged fire briefly overnight.
The resident added that Saud-led coalition jets were heard overhead on Saturday morning.
In addition to the withdrawal of fighters from Hodeida, the agreement included a planned prisoner swap involving some 15,000 detainees.
A "mutual understanding" was also reached to facilitate aid deliveries to Yemen's third city Taiz – under the control of Saudi-backed forces but besieged by Houthis.
The two sides have agreed to meet again in late January for more talks to define the framework for negotiations on a comprehensive peace settlement.
The war between the Houthis and troops loyal to former president Abd-Rabboh Mansour Hadi escalated in March 2015, when he fled into Saudi exile and the Saudi-led coalition intervened.
Since then, the war has killed some 10,000 people, according to the World Health Organization, although human rights groups say the real death toll could be five times as high.
More than 22 million people – three quarters of the population –now depend on humanitarian assistance to survive.
Yemenis struggling to survive such conditions are also confronted with a collapsed economy, leaving civil servants and teachers without pay for months.