The Islamic republic made no announcement about accepting the appointment of an ambassador for the Houthis, who control the Yemeni capital Sanaa and much of the north.
The Houthi-run Al-Masirah TV said late on Saturday that a "presidential decree was issued appointing Ibrahim Mohammed Mohammed al-Dailami as an ambassador extraordinary and plenipotentiary for the republic of Yemen to the Islamic republic of Iran".
Yemeni President Abedrabbo Mansour Hadi severed diplomatic relations with Iran in October 2015, accusing Tehran of providing military aid to the rebels.
Tehran has denied the accusation but publicly offers strong political backing to the Shia Houthis.
The Yemeni government denounced the naming of an ambassador.
"The exchange of diplomatic relations between Tehran regime and the Houthi militias breaches the international laws and norms and contravenes United Nations Security Council resolutions related to the Yemen crisis," the government said in a statement on Twitter.
It said the step has exposed the hidden relationship between the Houthis and Iran.
The announcement comes after Iran's supreme leader Ayatollah Ali Khamenei held talks in Tehran on Tuesday with a Huthi delegation headed by rebel spokesman Mohammed Abdul Salam.
Khamenei renewed his support for the Houthis and accused Iran's foes of a "plot" to partition the country.
Yemen has witnessed intense fighing between the Houthis and government forces since the rebels entered Sanaa in September 2014 and drove Hadi into exile in Saudi Arabia.
A Saudi-led coalition intervened in March 2015 to support the government forces.
The conflict has claimed the lives of tens of thousands of people and displaced around 3.3 million since 2015.
Two-thirds of the population - about 20 million people - require humanitarian support, according to the United Nations.
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