The Yemeni foreign ministry announced a day earlier that it had declared George Abu al-Zulof persona non grata, accusing him of lacking impartiality in his reporting on the human rights situation.
UN Secretary-General Ban Ki-moon had urged the Saudi-backed government to reverse its decision and allow Zulof to stay, warning that Yemen would be falling short of its obligations by "impeding" UN human rights work.
Diplomats said Yemen's foreign ministry had notified the United Nations that the decision had been reversed and was to send official confirmation.
Relations between the United Nations and the government of President Abedrabbo Mansour Hadi have become testy over the world body's increasingly vocal criticism of the Saudi-led coalition's air campaign in Yemen.
Earlier on Friday, Ban said he had received "troubling reports" of cluster bomb attacks on January 6 on the rebel-held capital Sanaa and warned that the use of these munitions "may amount to a war crime."
Cluster bombs are banned under a 2008 international convention, although Saudi Arabia and the United States are not signatories.
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The UN chief said he was "deeply concerned about the intensification of coalition airstrikes and ground fighting and shelling in Yemen, despite repeated calls for a renewed cessation of hostilities."
He is "particularly concerned about reports of intense airstrikes in residential areas and on civilian buildings in Sanaa, including the Chamber of Commerce, a wedding hall and a center for the blind," said the statement.
UN envoy Ismail Ould Cheikh Ahmed was in Riyadh on Friday for talks on renewing a ceasefire in Yemen, which faces the threat of famine amid the dire humanitarian crisis.
Yemen descended into chaos when the coalition began airstrikes in March to push back Iran-backed Huthi rebels who had seized Sanaa.
More than 5,800 people have been killed and 27,000 wounded since then, according to UN figures.
Yemen's government sat down with the rebels and their allies in Switzerland last month for six days of talks that ended with no major breakthrough.
The UN envoy has called for a new round of talks on January 14 but the sides have yet to confirm that they will attend.