The Mahan Air plane arrived in Sanaa carrying a team from the Iranian Red Crescent and medical aid, an aviation official told AFP.
Senior Iranian diplomats were on hand to welcome the flight -- the first between the two countries in many years.
Yemen's official Saba news agency, which is controlled by the Shiite militiamen who overran Sanaa in September, said Mahan Air and Yemenia would each operate 14 weekly flights under the accord.
Western-backed President Abedrabbo Mansour Hadi, who last weekend escaped house arrest by the Huthis in Sanaa, slammed the agreement as "illegal," according to an aide.
"Those who signed it will be held accountable," Hadi said during a meeting with tribal chiefs in the southern city of Aden where he is now based.
Tehran has repeatedly been accused of backing the Huthi militia, also known as Ansarullah.
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Meanwhile, Saba reported that a Huthi delegation led by the head of the "Ansarullah political council", Saleh al-Sammad, would travel to Tehran on Sunday for an "official" visit.
"The delegation which includes an economic delegation, will hold talks with Iranian government officials to discuss means of strengthening economic, political and other means of cooperation between both countries," Sammad told Saba.
The visit is part of efforts to "open new horizons in relations with countries that respect the will of the Yemeni people", said Sammad.
US Secretary of State John Kerry charged last week that "critical" support of the militia by Shiite-dominated Iran had "contributed" to the collapse of Yemen's government.
Iran rejected Kerry's "blame game," insisting that foreign intervention in Yemen would only "further complicate the situation"
The Huthis, who have long clashed with central authorities, descended from their power base in northern Yemen to seize Sanaa in September.
After moves to expand into southern and central Yemen were checked by fierce resistance from Al-Qaeda and from Sunni tribesmen, the militia grabbed the seats of power in Sanaa in February.